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PRINCIPLES OF GEOPHYSICS

Abdullah M. Al-Amri

Dept. of Geology & Geophysics

King Saud University, Riyadh

@gmail.comgeoalamri. alamri.com-www.a

2018

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Free Advice

Group study. is strongly encouraged. Interaction with peers and instructors is very beneficial to your learning and digesting the material. Make good use of it. Discuss the problems with the TA. Ask questions. It is recommended that you put in at least 2 hours of study for each 1 hour of lecture. It is very useful to read ahead, before the material comes up in the classroom. Feel free to ask questions, make comments or just express your opinions. Think. The assigned problem sets present an opportunity for you to think about and apply the material presented in the lectures and in some cases to learn new material. Start them early in the week so that you can think about them and exercise your creative potential. Note that solving a problem does not only consist of inserting numbers into equations and crunching out new numbers. Strive for 100% on the assignments utilizing all the resources and opportunities available to you. Expanding your mind. Learning is a process of expanding your mind. This is attained by developing new connections between neurons in your brain and strengthening selected neural pathways. Be persistent and don’t give up when you come to the inevitable hard sections. For some of you that might be at the beginning, for others the resistance might increase with time. Hang in there. Don’t Copy. Copying the solutions to assigned problems from other sources is not only discouraged. It is not professional, it does not reflect well on you as a future geophyscist, and it is detrimental to your character and professional career. It is an activity that shows disrespect for you, for your classmates, and for your instructors. If you have questions, ask the instructor or the TAs. If you follow the lectures, keep up with the homework problems, and ask questions to your classmates, TAs and the instructor, you will be on your way to mastering the material. Persistence and motivation are the only prerequisites to success. Make it a game to master new skills and knowledge. Be courageous in facing new challenges.

Measured objectively, what a man can wrest from Truth by passionate striving is utterly infinitesimal. But the striving frees us from the bonds of the self and makes us comrades of those who are the best and the greatest. Albert Einstein

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INTRODUCTION

Geophysics is an interdisciplinary physical science concerned with the

nature of the earth and its environment and as such seeks to apply the

knowledge and techniques of physics, mathematics and chemistry to

understand the structure and dynamic behavior of the earth and its

environment. The required sequence of Mathematics, Physics and

Geophysics courses is designed to provide a basic structure on which to

build a program with science electives normally selected from Geology,

Astronomy, Oceanography, Mathematics, Physics and Chemistry courses.

Geophysics is the science which deals with investigating the Earth, using

the methods and techniques of Physics. The physical properties of earth

materials (rocks, air, and water masses) such as density, elasticity,

magnetization, and electrical conductivity all allow inference about those

materials to be made from measurements of the corresponding physical

fields - gravity, seismic waves, magnetic fields, and various kinds of

electrical fields. Because Geophysics incorporates the sciences of Physics,

Mathematics, Geology (and therefore Chemistry) it is a truly

multidisciplinary physical science.

The two great divisions of Geophysics conventionally are labeled as

Exploration Geophysics, and Global Geophysics. In Global

Geophysics, we study earthquakes, the main magnetic field, physical

oceanography, studies of the Earth's thermal state and meteorology

(amongst others!). In Exploration Geophysics, physical principles are

applied to the search for, and evaluation of, resources such as oil, gas,

minerals, water and building stone. Exploration geophysicists also work in

the management of resources and the associated environmental issues.

Geophysics contributes to an understanding of the internal structure and

evolution of the Earth, earthquakes, the ocean and many other physical

phenomena. There are many divisions of geophysics, including

oceanography, atmospheric physics, climatology, petroleum geophysics,

environmental geophysics, engineering geophysics and mining geophysics.

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Geophysical Exploration Techniques

Geophysical methods are divided into two types : Active and Passive

(Natural Sources): Incorporate measurements of Passive methods

natural occurring fields or properties of the earth. Ex. SP, Magnetotelluric

(MT), Telluric, Gravity, Magnetic.

(Induced Sources) : A signal is injected into the earth Active Methods

and then measure how the earth respond to the signal. Ex. DC. Resistivity,

Seismic Refraction, IP, EM, Mise-A-LA-Masse, GPR.

Common Applications

- oil and gas exploration

- mineral exploration

- diamond exploration (kimberlites)

- hydrogeology

- geotechnical and engineering studies

- tectonic studies

- earthquake hazard assessment

- archaeology

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CHAPTER 1

FUNDAMENTAL CONSIDERATIONS

- Stress - Strain Relationship

- Elastic Coefficients

- Seismic Waves

- Huygen and Fermat principles

- Snell's Law in Refraction

Problem Set – 1

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THEORY OF ELASTICITY

Stress is the ratio of applied force F to the area across which it is acts.

Strain is the deformation caused in the body, and is expressed as the ratio of

change in length (or volume) to original length (or volume).

Triaxial Stress

Stresses act along three orthogonal axes, perpendicular to faces of solid, e.g.

stretching a bar:

Pressure

Forces act equally in all directions perpendicular to faces of body, e.g.

pressure on a cube in water:

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Strain Associated with Seismic Waves Inside a uniform solid, two types of

strain can propagate as waves:

Axial Stress : Stresses act in one direction only, e.g. if sides of bar fixed:

Change in volume of solid occurs.

Associated with P wave propagation

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Shear Stress : Stresses act parallel to face of solid, e.g. pushing along a

table:

No change in volume.

Fluids such as water and air cannot support shear stresses.

Associated with S wave propagation.

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Stresses on a solid in 3 dimensions

Stress = Force applied to a body per unit area (s = F/dS).

The stress can be expressed in two sets of components:

-Normal stress (n), perpendicular to the surface of the body (c.f.

pressure) -

Shear stress (t) acting parallel to the surface

of the body For each surface one can define 3 orthogonal

components of stress. The surfaces themselves can be defined as 3

orthogonal components _ definition of 9 components of

stress (direction of the force and direction of the surface on which it acts).

For each body, it is possible to define 3 axes for which shear stresses are

zero and only the normal stresses exist (using geometrical

transformations). These axes are called the principal axes, and the

corresponding normal stresses are the principal stresses.

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If all 3 principal stresses are equal, the body is subjected to a pressure

(lithostatic pressure in the case of solid rock).

Pressure = (sum of principal stresses)/3

Conventions for directions:

Stresses towards the interior: compression

Stresses towards the exterior: tension (extension, dilatation)

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Hooke’s Law

Hooke’s Law essentially states that stress is proportional to strain.

At low to moderate strains: Hooke’s Law applies and a solid body is

said to behave elastically, i.e. will return to original form when stress

removed.

At high strains: the elastic limit is exceeded and a body deforms in a

plastic or ductile manner: it is unable to return to its original shape,

being permanently strained, or damaged.

At very high strains: a solid will fracture, e.g. in earthquake faulting.

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Constant of proportionality is called the modulus, and is ratio of stress to

strain, e.g. Young’s modulus in triaxial strain.

Elastic Moduli ( Constants )

(a) Young’s Modulus (E) – longitudinal strain proportional to longitudinal stress. E = F / A ÷ Dl / l

( b) Bulk Modulus (K) – describes the change of volume due to a change of pressure. K = P ÷ DV / V

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( c ) Shear Modulus (μ) – amount of angular deformation due to the application of a shear stress on one side of the object. μ = t / tan θ Note: μ = 0 in liquids (no rigidity).

(d) Axial modulus (ψ) – response to longitudinal stress, similar to

Young’s Modulus: Y = F /A ÷ Dl / l except that strain is uniaxial – no transverse strain

associated with the application of the longitudinal stress.

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Relationships between elastic moduli , Lamé coefficients

, and μ.

μ = shear modulus (as before)

= first Lamé coefficient (no direct physical interpretation)

Young’s Modulus: E = μ (3+ 2 μ ) ÷ (μ )

Bulk modulus: K = + 2/3 μ

Poisson’s Ratio: = 2 (μ )

Lamé 1 in terms of Poisson & Young

= E (1 + )(1 – 2)

Poisson's ratio ( Dimensionless ratio) is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Tensile deformation is considered positive and compressive deformation is considered negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio

= - etrans / elongitudinal

Poisson solid: material for which = μ, giving = 0.25

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SEISMIC WAVES

A. Body Waves

Seismic waves are pulses of strain energy that propagate in a solid. Two

types of seismic wave can exist inside a uniform solid:

A) P waves (Primary, Compressional, Push-Pull)

Motion of particles in the solid is in direction of wave propagation.

P waves have highest speed.

Volumetric change

Sound is an example of a P wave.

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B. S waves (Secondary, Shear, Shake)

Particle motion is in plane perpendicular to direction of propagation.

If particle motion along a line in perpendicular plane, then S wave is

said to be plane polarised: SV in vertical plane, SH horizontal.

No volume change

S waves cannot exist in fluids like water or air, because the fluid is

unable to support shear stresses.

v is the poisson’s ratio = 0 for a perfect fluid, so S-waves cannot propagate through fluids. Poisson’s ratio is theoretically bounded between 0 and 0.5 and for most rocks lies around 0.25, so typically VP/VS is about

1.7.

Vp /Vs ratios (hence Poisson’s Ratio) can be characteristic of rock type or

physical property, e.g.

-Felsic rocks _ lower Poisson’s Ratio

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-Mafic rocks _ higher Poisson’s Ratio

-Partial melt _ very high Poisson’s Ratio (S wave speeds are more strongly

affected by melt than P waves)

C. Surface Waves

Further a particle moves up and down vertically as well as in the direction

of the wave. In detail a particle traces an ellipse with a prograde rotation

as shown in the sketch below. The surface wave on an isotropic half -space

is known as a Rayleigh wave and it is similar in form to the surface wave on

a liquid half-space except that the particle motion is retrograde.

1. Rayleigh waves

Propagate along the surface of Earth

Amplitude decreases exponentially with depth.

Near the surface the particle motion is retrograde elliptical.

Rayleigh wave speed is slightly less than S wave: ~92% VS.

2. Love waves

Particle motion is SH, i.e. transverse horizontal

Dispersive propagation: different frequencies travel at different

velocities, but usually faster than Rayleigh waves.

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wave velocity and -, is tied to the SRVayleigh wave, The velocity of a R

) through the solution to the following PVPoisson’s ratio (and hence to

equation (White, 1983)

For typical values of Poisson’s ratio the Rayleigh wave velocity varies only

. S.Vfrom 0.91 to 0.93

Since it is observed that velocity generally increases with depth,

Rayleigh waves of high frequency penetrate to shallow depth and have low

velocity whereas Rayleigh waves of low frequency penetrate to greater

depth and have high velocity. The change in velocity with frequency is

known as dispersion. For a typical surface source of Rayleigh waves the

initiating disturbance has a broad frequency spectrum so the observed

surface motion at some distance from the source is spread out in time, with

low frequencies coming first and high frequencies coming later.

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Seismic velocity, attenuation and rock properties

Rock properties that affect seismic velocity

Porosity

Lithification

Pressure

Fluid saturation

• Velocity in unconsolidated near surface soils (the weathered layer)

• Attenuation

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Generally, the velocities depend on the elastic modulii and density

via:

Rock properties that affect seismic velocity

1) Porosity. A very rough rule due to Wyllie is the so called time

average relationship:

where φ is the porosity.

This is not based on any convincing theory but is roughly right when the

effective pressure is high and the rock is fully saturated.

2) Lithification.

Also known as cementation. The degree to which grains in a

sedimentary rock are cemented together by post depositional, usually

chemical, processes, has a strong effect on the modulii. By filling pore

space with minerals of higher density than the fluid it replaces the bulk

density is also increased. The combination of porosity reduction and

lithification causes the observed increase of velocity with depth of burial

and age.

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3) Pressure.

In general velocity rises with increasing confining pressure and then levels

off to a “terminal velocity” when the effective pressure is high. Finally even

at depth, as the pore pressure increases above hydrostatic, the effective

pressure decreases as does the velocity. Over pressured zones can be

detected in a sedimentary sequence by their anomalously low velocities.

4) Fluid saturation.

From theoretical and empirical studies it is found that the compressional

wave velocity decreases with decreasing fluid saturation. As the fraction of

gas in the pores increases, K and hence velocity decreases. Less intuitive is

also decreases with an increase in gas content. s the fact that V

Attenuation

It is observed that seismic waves decrease in amplitude due to spherical

spreading and due to mechanical or other loss mechanisms in the rock

units that the wave passes through.

The attenuation for a sinusoidal propagating wave is defined formally

as the energy loss per cycle (wave length) Δ E/E where E is the energy

content of the wave.

Mathematically, the propagating wave , get an added damping

term , so the solution becomes

2

[We can apply this to the definition of attenuation Δ E/E by substituting A

for the energy at two points at distance λ (the wavelength) apart and we

find

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frequency and that there is little dispersion. In fact to a good approximation

attenuation can be described by . With x in meters and f in

. So at one Hertz the amplitude falls to Hertz, a typical shale has a

uation may /e in 10 m. The atten0/e at 10 km. But at 1000 Hz it falls to A0A

be as much as 10 times greater in unconsolidated sediments. So

attenuation increases rapidly with decreasing wavelength.

Example : Consider attenuation is an unconsolidated medium with a

λ = 0.25 m, and α velocity of 250 m/sec and a frequency of 1000 Hz. Then,

×256. The wave would fall to 1/e of its initial amplitude when a = 157 3

= a

m.

Constraints on Seismic Velocity

Seismic velocities vary with mineral content, lithology, porosity, pore fluid

saturation, pore pressure, and to some extent temperature.

In igneous rocks with minimal porosity, seismic velocity increases with

increasing mafic mineral content.

In sedimentary rocks, effects of porosity and grain cementation are more

important, and seismic velocity relationships are complex.

Various empirical relationships have been estimated from either

measurements on cores or field observations:

1) P wave velocity as function of age and depth

km/s

where Z is depth in km and T is geological age in millions of years (Faust,

1951).

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2) Time-average equation

f and Vm are P wave velocities of pore fluid and rock

matrix respectively (Wyllie, 1958).

Usually Vf ≈ 1500 m/s, while Vm depends on lithology.

If the velocities of pore fluid and matrix known, then porosity can be

estimated from the measured P wave velocity.

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Waves and Rays

Considering a source at point O on a homogeneous half-space, the

resulting seismic P-wave propagates such that all the points of constant

phase lie on a hemisphere centered at O. The surface of all points of the

same phase is called a wave front although the inferred meaning is that

the phase in question is associated with some identifiable first arrival of the

wave. A more rigorous definition is that the wave front is the surface of all

equal travel times from the source. A cross section of such a hemispherical

spreading wave is shown in the following cartoon for two successive time

steps, t1 and 2t1.

The vector perpendicular to a wave front is defined as a ray. The ray in the

cartoon is directed along a radius from the source, but this is not always

the case. Rays are useful for describing what happens to waves when they

pass through an interface

Huygen’s Principle

Every point on a wavefront can be considered a secondary source of

spherical waves, and the position of the wavefront after a given time is the

envelope of these secondary wavefronts.

Treat all the points on a wavefront as point sources that generate secondary spherical wavefronts (‘wavelets’).

Useful for understanding reflection, refraction and diffraction of

seismic waves.

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•

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Snell’s Law

A wave incident on a boundary separating two media is reflected back into

the first medium and some of the energy is transmitted, or refracted, into

refraction and reflection is governed by the second. The geometry of

which relates the angles of incidence, reflection and refraction Snell’s Law

to the velocities of the medium.

The cartoon below illustrates the ray geometry for a P-wave incident on the

. The angles of incidence, 2and V1 locity Vboundary between media of ve

, respectively are the angles the ray 2and θ’, 1θ,1reflection and refraction, θ

makes with the normal to the interface.

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Snell’s law requires that the angle of reflection is equal to the angle of incidence.

the ray is bent towards the normal 1 Vthan is less2 Vif

the ray is bent away from the normal. 1 Vis greater than 2 Vif

the angle of refraction is greater than the ngle 1 Vis greater than 2 VIf

= 2 of incidence. The latter result can lead to a special condition where θ

. c

θ, critical angleof incidence for which this occurs is called the ° . The angle90

The critical angle is given by;

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When a P wave is incident on a boundary, at which elastic properties

change, two reflected waves (one P, one S) and two transmitted waves

(one P, one S) are generated.

Angles of transmission and reflection of the S waves are less than the P

waves. Exact angles of transmission and reflection are given by:

p is known as the ray parameter.

There are two critical angles corresponding to when transmitted P and S

waves emerge at 90°.

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Diffractions

Reflection by Huygen’s Principle

When a plane wavefront is incident on a plane boundary, each point of the

boundary acts as a secondary source. The superposition of these secondary

waves creates the reflection.

Diffraction by Huygen’s Principle

If interface truncates abruptly, then secondary waves do not cancel at the

edge, and a diffraction is observed.

This explains how energy can propagate into shadow zones.

A small scattering object in the subsurface such as a boulder will

produce a single diffraction.

A finite-length interface will produce diffractions from each end, and

the interior parts of the arrivals will be opposite polarity.

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PROBLEM SET - 1

1. A steel beam is placed vertically in the basement of a building to keep the floor above from sagging. The load on the beam is 5.8 x104 N and the length of the beam is 2.5 m, and the cross-sectional area of the beam is 7.5 x 10-3 m2. Find the vertical compression of the beam. 2. A 0.50 m long string, of cross- sectional area 1.0 x10-6 m2, has a Young’s modulus of 2.0 x 109 Pa. By how much must you stretch a string to obtain a tension of 20.0 N? 3. The upper surface of a cube of gelatin, 5.0 cm on a side, is displaced by 0.64 cm by a tangential force. If the shear modulus of the gelatin is 940 Pa, what is the magnitude of the tangential force? 4. An anchor, made of cast iron of bulk modulus 60.0 x 109 Pa and a volume of 0.230 m3, is lowered over the side of a ship to the bottom of the harbor where the pressure is greater than sea level pressure by 1.75 x 106 Pa. Find the change in the volume of the anchor. 5. 1. AN ARKOSE HAS A DENSITY OF 2.62 G/CM, A YOUNG MODULUS OF 0.16X10 N/M , AND A POISSON'S RATIO OF 0.29 . TWELVE GEOPHONES ARE ARRANGED ALONG A LINE AT 10 M INTERVAL. THE SHOT POINT IS LOCATED 5 M FROM THE FIRST GEOPHONE IN THE LINE. CONSTRUCT A GRAPH THAT ILLUSTRATES TIME OF ARRIVAL AGAINST GEOPHONE POSITION FOR THE P-WAVE , S-WAVE AND SURFACE WAVE.

THE VOLUM OF ALUMINUM BLOCK WAS PLACED UNDER HYDRAULIC PRESSURE IS . 6

A. 3 0.4 M A. FIND THE CHANGE IN VOLUM OF THE ALUMINUM WHEN SUBJECTED TO PRESSURE

AND THE RIGIDITY 2. THE BULK MODULUS IS 0.85 X 1011 N/M2N/M 72.1 X 10 OF

.2N/M 11MODULUS IS 0.36 X 10

B. B. WHAT IS THE CUBICAL DILATATION

C. FIND YOUNG’S MODULUS, COMPRESSIBILITY, AND POISSON’S RATIO.

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7. A 15 HZ SEISMIC WAVE TRAVELLING AT 5.5 KM/SEC PROPAGATES FOR 1500 M

THROUGH A MEDIUM WITH AN ABSORPTION COEFFICIENT OF 0.3 dB . WHAT IS THE WAVE ATTENUATION IN dB DU E SOLELY TO ABSORPTION.

8. CALCULATE THE AMPLITUDE OF THE REFLECTED AND TRANSMITTED P- AND S- WAVES WHERE THE INCIDENT P-WAVE STRIKE THE INTERFACE FROM A WATER

0VELOCITY =0, DENSITY = 1.20 g/cc) AT 25-K/S, 5=2.5 VELOCITY -LAYER ( PWHEN THE SEAFLOOR IS:

A. SOFT ( P=3K/S, S=1.5 K/S. DENSITY2.O g/cc

B. HARD ( P= 4 K/S, 5= 2.5 K/S, DENSITY =2.5 g/cc

030 N ANGLE OF INCIDENCEREPEAT FOR AC.

9. A rock sample is taken to the lab and is subjected to a uniaxial stress (that is, it is

stressed in only one direction with the remaining directions free). As a result of the

stress, the length of the sample increases by 3% and the width decreases by 1%.

What is the ratio of the P wave velocity to the S wave velocity in this sample?

10. A material has a shear modulus of 8.8×109 Pa, a bulk modulus of 2.35×1010 Pa, a

density of 2200 kg/m3 and a quality factor Q = 100.

a) What are the P-wave velocity and S-wave velocity of the medium, in units of km/s

b) If a P-wave of frequency 10 Hz has a displacement amplitude of 1 μm at a distance

of 10 m from the source, what would be the wave amplitude at 100 m?

11. Near-surface fresh water in a Lake Superior has been observed to have a P-wave

velocity of 1435 meters/sec. Estimate its bulk modulus, assuming it is pure water.

12. A laboratory has determined that the Gabbro has the following properties:

Bulk modulus= 0.952130 X 1012 dyne/cm2

Shear modulus=0.403425 X 1012 dyne/cm2

Density=2.931 gm/cc

Determine the (a) shear wave velocity, the (b) compressional wave velocity, and

(c) Poisson's ratio for this rock.

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CHAPTER 2

SEISMIC REFRACTION METHOD

- Fundamentals

- Two Horizontal Interfaces

- Dipping Interfaces

- The Non ideal Subsurface

- The Delay-Time Method

- Field Procedures & Interpretation

Problem Set - 2

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Seismic Refraction

A signal, similar to a sound pulse, is transmitted into the Earth. The signal

recorded at the surface can be used to infer subsurface properties. There

are two main classes of survey:

Seismic Refraction: the signal returns to the surface by refraction

at subsurface interfaces, and is recorded at distances much greater

than depth of investigation.

Seismic Reflection: the seismic signal is reflected back to the

surface at layer interfaces, and is recorded at distances less than

depth of investigation.

Applications

Seismic Refraction

Rock competence for engineering applications

Depth to Bedrock

Groundwater exploration

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Correction of lateral, near-surface, variations in seismic reflection

surveys

Crustal structure and tectonics

Seismic Reflection

Detection of subsurface cavities

Shallow stratigraphy

Site surveys for offshore installations

Hydrocarbon exploration

Crustal structure and tectonics

Travel Time Curves

Analysis of seismic refraction data is primarily based on interpretation of

critical refraction travel times. Plots of seismic arrival times vs. source-

receiver offset are called travel time curves.

Example

Travel time curves for three arrivals shown previously:

Direct arrival from source to receiver in top layer

Critical refraction along top of second layer

Reflection from top of second layer

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Critical Distance

Offset at which critical refraction first appears.

Critical refraction has same travel time as reflection

Angle of reflection same as critical angle

Crossover Distance

Offset at which critical refraction becomes first arrival.

Field Surveying

Usually we analyze P wave refraction data, but S wave data occasionally

recorded

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1. Horizontal Interfaces: Two Layers

For critical refraction at top of second layer, total travel time from source S

to receiver G is given by:

Hypoteneuse and horizontal side of end 90o-triangle are:

and respectively.

So, as two end triangles are the same:

At critical angle, Snell’s law becomes:

Substituting for V1/ V2, and using cos2 2

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This equation represents a straight line of slope 1/V2 and intercept

Interpretation of Two Layer Case

From travel times of direct arrival and critical refraction, we can find

velocities of two layers and depth to interface:

1. Velocity of layer 1 given by slope of direct arrival

2. Velocity of layer 2 given by slope of critical refraction

3. Estimate ti from plot and solve for Z:

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Depth from Crossover Distance

At crossover point, traveltime of direct and refraction are equal:

Solve for Z to get:

[Depth to interface is always less than half the crossover distance]

Xcritical = Minimum distance for refraction arrival = 2 z1 tan ic

2. Dipping Interfaces : Two Layer Case

When a refractor dips, the slope of the traveltime curve does not represent

the "true" layer velocity:

shooting updip, i.e. geophones are on updip side of shot, apparent

refractor velocity is higher

shooting downdip apparent velocity is lower

To determine both the layer velocity and the interface dip, forward and

reverse refraction profiles must be acquired.

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Note: Travel times are equal in forward and reverse directions for

switched, reciprocal, source/receiver positions.

Geometry is same as horizontal 2-

extra time delay at D. So traveltime is:

Formulae for up/downdip times are (not proved here):

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where Vu/ Vd and tu/ td are the apparent refractor velocities and intercept

times.

;

Can now solve for dip, depth and velocities:

C:

;

[V1 is known from direct arrival, and Vu and Vd are estimated from the

refraction traveltime curves]

2) Can find layer 2 velocity from Snell’s law:

1. Can get slant interface depth from intercept times, and convert to

vertical depth at source position:

;

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3. Faulted Planar Interface ( Diffraction )

If refractor faulted, then there will be a sharp offset in the travel time

curve:

Can estimate throw on fault from offset in curves, i.e. difference between

two intercept times, from simple formula:

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Delay Times in Refraction

For irregular travel time curves, e.g. due to bedrock topography or glacial

fill, much analysis is based on delay times.

Total Delay Time . Difference in travel time along actual ray path and

projection of ray path along refracting interface:

;

Total delay time is delay time at shot plus delay time at geophone:

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For small dips, can assume x=xI and:

Refractor Depth from Delay Time

If velocities of both layers are known, then refractor depth at point A can

be calculated from delay time at point A:

Using the triangle to get lengths in terms of z:

Using Snell’s law to express angles in terms of velocities:

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Simplifying:

So refractor depth at A is:

Blind layer problem

Blind layers occur when there is a low velocity layer (LVL). Head waves

only occur for a velocity increase. Thus, there will be no refraction from

the top of the LVL and this layer will not be detected on the time-distance plot.

This is shown below.

Hidden layer problem

Hidden layers result when there is a velocity increase with layer depth, but

the head wave from the top of one layer is never the first arrival on a

time-distance plot. Head waves from a deeper layer arrive at the detectors

before the arrivals from this layer. Two factors can cause hidden layers: 1)

the layer is very thin or 2) there is only a small velocity increase at the top

of the layer. This is shown below. It is sometimes possible to recognize

hidden layers by looking for arrivals after the first arriving energy.

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PROBLEM SET - 2

Q1. Consider a case where there is a continuous velocity increase

with depth, as is commonly observed in the Earth. The propagation of

seismic waves can be investigated by assuming that the subsurface is made

up of infinitely thin layers of uniform velocity. Sketch the expected ray

paths and travel time curve.

Remember that Snell’s Law requires that the ray parameter is constant: P

= sinθ/ v

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2. Given the reversed refraction observations (travel time vs. distance curves) shown

below, calculate the velocities and depths to the interfaces. Calculate the dip angles of

the interfaces.

3. Given the following schematic travel-time curve, describe a subsurface structure

and/or velocity changes that may explain them.

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4. A seismic refraction survey was conducted along an abandoned railroad grade about

2.5 miles southeast of the town of Osakis. The railroad grade is known to be resting on

Pleistocene glacial deposits. A 12 channel system was used with an sledge hammer for

an energy source, and the following first break times were picked from the traces.

Distance First break time(meters) (milliseconds)

5 14

15 23

25 30

35 36.75

45 42

55 50

65 54.5

75 61

85 65.5

95 66.5

105 70

115 73.25

A reversed profile yielded essentially identical results, so we can assume horizontal

layering. It is assumed that the first and second layers will represent the grade fill and

the glacial deposits, respectively.

Plot the travel time relationships and estimate the velocities of the first two layers (in

meter/second). What is the thickness of the grade fill?

Based on your velocity estimate for the second layer, do you think the glacial deposits

are saturated or unsaturated (below or above the water table)?

Do you have any evidence of bedrock (ie a third layer) below the glacial deposits? If so,

what is its velocity (in meters/second) and depth?

5. SUPPOSE THAT A REVERSED REFRACTION SURVEY ( USING SHOTS A AND B )

INDICATED VELOCITIES V1 = 1500 M/SEC. AND V2 = 2500 M/SEC. FROM SHOT A

AND VELOCITIES V1 = 1500 M/SEC AND V2 = 3250 M/SEC. FROM SHOT B.

FIND THE DIP OF REFRACTOR. WHAT WOULD BE THE CHANGES IN VELOCITIES IF

THE FEFRACTOR HAD A SLOPE 10 DEGREES LARGER THAN THE ONE YOU

COMPUTED.

50

6. Construct a travel time curve to a distance of 120 m for a structure with an 10 m thick soil layer with P-wave velocity 500 m/s over a saturated layer 20 m thick with P-wave velocity 1500 m/s over bedrock with velocity 3000 m/s. From the graph, what are the 2 crossover distances?

7. Construct a travel time curve for the following data for both the forward and reverse profiles. Evaluate slopes and intercept times, and use those values to determine the subsurface structure for the first 2 layers, and then estimate the properties of the bottom layer. Offsets are in meters and times are in milliseconds.

Offset x 5 10 15 20 25 30 35 40 45 50 55 60 Forward 8.3 16.7 25.0 33.3 41.7 50.0 58.3 66.7 72.5 75.1 77.7 80.3 Reverse 8.3 16.7 25.0 33.3 40.7 44.3 48.0 51.6 55.3 58.9 62.6 66.3

8. The following data are from a profile over a buried steep fault scarp underlying alluvium. Use the data to determine velocities for the alluvium and bedrock and the throw and approximate position of the buried fault step. Offsets are in meters and times are in milliseconds.

Offset x 5 10 15 20 25 30 35 40 45 50 55 60 Forward 3.6 7.1 10.7 14.3 17.9 21.4 23.0 24.0 24.9 25.8 26.7 27.7 Reverse 3.6 7.1 10.7 14.3 17.9 21.4 25.0 28.6 30.4 25.8 26.7 27.7

9. FROM SNELL’S LAW, CALCULATE THE CHANGE IN DIRECTION OF A SEISMIC

WAVE WHEN IT REFRACTED FROM A SANDSTONE STRATUM ( V = 4000 M/SEC AND 350 M THICK) INTO A LIMESTONE STRATUM (V=6000 M/SEC ) FOR EACH OF THE FOLLOWING ANGLES OF INCIDENCE 0, 15, 25, 35, 45, AND 60.

WHAT IS THE CRITICAL ANGLE. WHAT IS THE MINIMUM DISTANCE FOR REFRACTION ARRIVALS WHAT IS THE CROSS- OVER DISTANCE

WITH THE THICKNESS OF SANDSTONE LAYERCO COMPARE THE VALUES OF X WHAT IS THE NMO AND REFLECTION TRAVEL TIME

51

CHAPTER 3

SEISMIC REFLECTION METHOD

- A Single Subsurface Interface

- Analysis of Arrival Times

- Normal Move out

- Determining of Velocity & Thickness

- Dipping Interface

- Common Field Procedures

- Velocity Analysis

- Applications in Petroleum exploration

Problem Set - 3

52

SEISMIC REFLECTION

1. Reflection at normal incidence

Consider two horizontal layers that have different seismic velocities (v) and

densities (ρ). A P-wave with amplitude Ai travels downward through the

upper layer and encounters the interface between the layers at 90° (normal

angle). This produces two new P-waves: a reflected P-wave that travels

upward through Layer 1 and a transmitted P-wave that enters Layer 2.

The reflection co-efficient is the ratio of the amplitudes of the reflected

and incident waves: R = Ar/Ai

Similarly, the transmission co-efficient is the ratio of the amplitudes of

the transmitted and incident waves: T = At/Ai

The amount of energy that is partitioned into transmission and reflection

depend on the angle between the incident wave and interface and on the

acoustic impedance (Z) of each layer:

Z1 = ρ1v1 and Z2 = ρ2v2

For normal incident waves, it can be shown that:

R = ρ2v2 - ρ1v1 / ρ2v2 + ρ1v1 = Z2 – Z1 / Z2 + Z1

T = 2 ρ1v1 / ρ2v2 + ρ1v1 = 2Z1 / Z2 + Z1

These are the Zoeppritz equations. There are also more complicated

forms of the Zoeppritz equations that can be used for any angle of

incidence.

53

These equations show that the reflection and transmission coefficients

depend on the difference in impedance between the two layers.

• if Z1 = Z2, there is no reflection. All energy is transmitted into the second

layer. This does not mean that ρ1=ρ2 and v1= v2! All that matters is that

ρ1v1= ρ2v2.

• R can have a value of +1 to -1. R will be negative when Z1 > Z2. A

negative value means that there will be a phase change of 180° in the

phase of the reflected wave (a peak becomes a trough). This is called a

negative polarity reflection.

• T is always positive – transmitted waves have the same phase as the

incident wave. T can be larger than 1.

• Reflection coefficients for the Earth are generally less than ±0.2, with

maximum values of ±0.5. Most energy is transmitted, not reflected.

Case 1: An increase in velocity with depth

A 600 m thick layer of sandstone overlies a granite basement with a higher

velocity. A seismic wave is generated at the surface and travels vertically

downward. At the sandstonegranite interface, the incident wave is split into

a reflected wave and transmitted wave. The amplitude of the reflected and

transmitted waves (Ar and At) can be calculated from the Zoeppritz

equations. Assume that Ai = 1.0 and that there is no geometrical

54

spreading, attenuation, or scattering. Velocity and density are constant

within each layer.

First, calculate the impedance of each layer:

Z1 = ρ1v1 = 2700 × 4.1 = 11,070 (kg km s-1 m-3)

Z2 = ρ2v2 = 2700 × 5.6 = 15,120 (kg km s-1 m-3)

The reflection and transmission co-efficients are then:

R = 0.15 , T = = 0.85

The amplitude of the two waves are:

Ar = R x Ai = 0.15 At = T x Ai = 0.85

Consider a seismic survey configuration where you have a seismic source

and a receiver on the ground next to each other. The receiver will record

seismic waves that travel directly between the source and receiver, as well

as seismic waves that are reflected upward to the surface. In this case,

only one reflected wave will be recorded. The time at which it arrives at the

receiver is:

Time = 2 x 600 / 4100 = 0.29s

The seismic record will look like this:

55

More than two layers:

The same Zoeppritz equations can be applied to models with more than

two layers.

Case 1: Velocity increase with depth

In this case, there will be two reflected waves that are recorded by the

seismic station (also called arrivals).

A1 is the wave that is reflected from Interface A.

A2 is the wave that is transmitted through Interface A, reflected from

Interface B, transmitted through Interface A, and then recorded at the

surface

56

.

Arrival A1:

Amplitude: given by the reflection co-efficient at interface A (RA):

Z1 = 2700 × 3.1 = 8370 Z2 = 2700 × 4.5 = 12150

Therefore: RA = 0.18 , Arrival time: 0.26s

Arrival A2:

To calculate the arrival time and amplitude of A2, we need to consider all

the interfaces that it has encountered between the source and receiver.

1. Transmitted through Interface A.

The amplitude of the transmitted wave at A is TA = 0.82

57

2. Reflected at interface B.

The reflection amplitude depends on:

• The amplitude of the incident wave. The incident wave is the one that

was transmitted through Interface A: TA = 0.82

• Reflection co-efficient from Layer 2 to Layer 3 (RB)

Z2 = 12150 Z3 = 2700 × 6.8 = 18360

RB = 0.2

Therefore, the amplitude of the reflected wave is: TA × RB = 0.16

3. Transmitted through Interface A.

The amplitude of the transmitted wave is the product of:

• the amplitude of the reflected wave from Interface B ( = TA × RB

=0.16)

• transmission co-efficient from Layer 2 to Layer 1

Therefore the final amplitude of A2 will be: TA × RB × T’A = 0.16 ×

1.18 = 0.19

The total travel time of A2 will be: 0.13 + 0.40 + 0.13s = 0.66s

The seismic record will look like:

58

Reflection time- distance plots

Consider a source (shot point) at point A with geophones spread out along

the x-axis on either side of the shot point.

This is the equation of a hyperbola symmetric about the t axis. The travel

time plot for the direct wave arrivals and the reflected arrivals are shown in

the following plot. The first layer is 100 m thick and its velocity is 500 m/s.

way zero -, is the twoiThe intercept of the reflected arrival on the t axis, t

59

offset time and for this model is equal to 400ms. At large offsets the

. 1hyperbola asymptotes to the direct wave with slope 1/V

In most seismic reflection surveys the geophones are placed at offsets

small compared to the depth of the reflector. Under this condition an

approximate expression can be derived via:

60

Since is less than 1, the square root can be expanded with the

binomial expansion. Keeping only the first term in the expansion the

following expression for the travel time is obtained:

This is the basic travel time equation that is used as the starting point for

the interpretation of most reflection surveys.

61

Moveout

A useful parameter for characterizing and interpreting reflection arrivals is

the moveout, the difference in travel times to two offset distances. The

following expanded plot of one side of the hyperbola of the previous

reflection plot shows the moveout, Δt, for two small offsets.

62

yields the 2 and x1 Using the small offset travel time expression for x

following expression for the moveout: , is a special term used for the moveout nThe normal moveout (NMO), Δt

The NMO for an offset x is then: is zero.1 when x

, the velocity is determined via: i With the value of the intercept time, t

For a given offset the NMO decreases as the reflector depth increases

and/or as the velocity increases.

In a layered medium the velocity obtained from the NMO of a deep

reflector is an average of the intervening layer velocities. Dix (1955) found

that the root-mean-square velocity defined by:

is the travel time in layer i is the best i is the velocity in layer i and ti where V

average to use.

63

In interpretation the NMO’s for successive reflections are used to obtain the velocities rms average velocity to each reflector. Assuming these are the V

defined above then Dix (1955) showed that the velocity in the layer

layer is given by: th

1-and nth

bounded by the n

Dip moveout

If the interface is dipping as in the figure below the up-dip and down-dip travel times are changed by an amount dependant on the dip angle θ. The time-distance plot is still a hyperbola but the axis of symmetry is shifted up-dip by 2h sinθ. (Shown by the dashed line in the figure. Note also that the depth is still the perpendicular distance from the interface to the shot point). The binomial expansion for the travel time for small offsets becomes:

For geophones offset a distance x up-dip and down-dip, the dip moveout is defined as:

For small dips when the dip moveout yields the dip via;

64

The velocity can be obtained with sufficient accuracy by averaging the velocities obtained in the usual manner from the up-dip and down-dip NMO’s.

65

Common Mid-Point Gathers

There are two disadvantages to using only a shot gather for analysis:

(1) Reflections tend to have a low amplitude (generally less than 20% of

the incident wave amplitude). This means that noise in the seismic data can

obscure reflections.

(2) Each reflection occurs at a different point on the interface. The analysis

of shot gathers assumes uniform horizontal layers. If there are significant

lateral variations in structure, this assumption is no longer valid and the

analysis can result in errors.

These problems can be overcome by using shots from a number of

different points and multiple detectors. The source and detectors are

moved in between shots.

From the complete data set, a subset of traces are chosen that have a

common reflection point. The reflection point is taken to be halfway in

between the shot and the detector.

• this is valid for areas with horizontal layering

• if the reflection occurs at a dipping interface, this is an approximation, but

does not introduce large errors

66

The collection of traces with the same reflection point is called a common mid-point gather (CMP gather) or common depth point (CDP) gather.

67

PROBLEM SET - 3

1. Consider a high velocity layer that overlies a low velocity

layer.

A. What are the amplitudes of the reflected and transmitted waves?

B. At what time will the reflected wave arrive back at the surface? What

is its polarity?

C. What will the seismic record at the surface look like?

68

2. Consider a case with a low velocity layer. This could

represent a gas- filled layer within high velocity rocks. What

are the first three arrivals (after the direct P- wave)?

Note : The corresponding seismic record will be:

69

3. CALCULATE THE REFLECTION AND TRANSMISSION COEFFICIENTS FOR NORMAL

INCIDENCE ON EACH BOUNDARY WITH THE FOLLOWING MATERIAL PROPERTY

CONTRASTS. WHAT PERCENT OF THE ENERGY IS REFLECTED AND

TRANSMITTED AT EACH INTERFACE.

VELOCITIES FT/S. Density

VERY STRONG REFLECTOR 11000 & 15000 NONE

GOOD REFLECTOR 14000 & 15000 NONE

WEAK REFLECTOR 8000 & 8200 NONE

SOFT OCEAN BOTTOM NONE 1.0 & 2.0

HARD OCEAN BOTTOM 5000 & 10000 1.0 & 2.5

WEATHERED OVER UNWEATH.

MATERIAL 1600 & 6000 1.6 & 2.0

SAND WITH 30% POROSITY

OVER THE SAME SAND WITH

GAS-FILLED PORES. 6000 & 9000 1.4 & 2.4

4. Seismic waves with a dominant frequency of 50 Hz travel through

sediments with a velocity of 3000 m/s.

• What is the smallest layer thickness that will be detected?

• If the deepest reflector is at a depth of 2000 m, what is the size of the

smallest horizontal feature that will be detected?

• What is the largest geophone spacing that should be used in the

survey?

70

CHAPTER 4

EARTHQUAKE SEISMOLOGY

- Definition and Historical review

- Classification of Earthquakes

- Earthquakes : Where and Why

- Causes of Earthquakes

- Earthquake Epicenter & Hypocenter

- Magnitude & Intensity

71

EARTHQUAKE SEISMOLOGY

COMPOSITION AND STRUCTURE OF THE EARTH

1. Crust. The outermost rock layer, divided into continental and

oceanic crust

a. Continental Crust (averages about 35 km thick; 60 km in

mountain ranges; diagram shows range of 20-70 km) Granitic

composition

b. Oceanic Crust (5 - 12 km thick; diagram shows 7-10 km

average)

Basaltic composition. Oceanic crust has layered structure (ophiolite

complex) consisting of the following:

1. Pillow basalts,

2. " Sheeted dikes " - interconnected basaltic dikes

3. Gabbro

2. Mantle (2885 km thick). The mantle stretches from the below

the crust to 2900 km below the surface. The upper part is partially

molten and the lower part is very dense. The main mantle rock is

peridotite.

Lithosphere = outermost 100 km of Earth . Consists of the crust plus

the outermost part of the mantle. Divided into tectonic or lithospheric

plates that cover surface of Earth

Asthenosphere = low velocity zone at 100 - 250 km depth in Earth

(seismic wave velocity decreases). Rocks are at or near melting point.

72

3. Outer core (2270 km thick)

S-waves cannot pass through outer core, therefore we know

the outer core is liquid (molten).

Composition: Molten Fe (85%) with some Ni, based on

studies of composition of meteorites. Core may also contain

lighter elements such as Si, S, C, or O.

Convection in liquid outer core plus spin of solid inner core

generates Earth's magnetic field. Magnetic field is also

evidence for a dominantly iron core.

4. Inner core (1216 km radius). Solid Fe (85%) with

some Ni - based on studies of meteorites

73

74

Plate Tectonics

The Earth's lithosphere is broken up into 6 major plates and about

14 minor ones. Oceanic plates are 50-100 km thick. Continental plates

are 100-250 km thick. Tectonic plates can include both continental and

oceanic areas. Six major plates are:

1. Indian-Australian 4. Antarctic 2. Pacific 5. African

3. American (N. and S) 6. Eurasian

75

o Plate Boundaries - Tectonic plates interact in various ways

as they move across the asthenosphere, producing

volcanoes, earthquakes and mountain systems. There are 3

primary types of Tectonic Plate boundaries: Divergent

boundaries; Covergent boundaries; and Transform.

o Divergent - Plates move away from one another, creating a

tensional environment. Characterized by shallow-focus

earthquakes and volcanism. Release of pressure causes

partial melting of mantle peridotite and produces basaltic

magma. Magma rises to surface and forms new oceanic

crust. Occur in oceanic crust (oceanic ridges) and in

continental crust (rift valleys). Continental rift valleys may

eventually flood to form a new ocean basin.

76

o Convergent - Plates move toward one another, creating a

compressional environment. Characterized by deformation,

volcanism, metamorphism, mountain building, seismicity,

and important mineral deposits. Three possible kinds of

convergent boundaries:

1. Oceanic-Oceanic Boundary - One plate is

subducted, initiating andesitic ocean floor volcanism on

the other. Can eventually form an island arc volcanic

island chain with an adjacent deep ocean trench.

Characterized by a progression from shallow to deep

focus earthquakes from the trench toward the island

arc (Benioff zone). May also form a back-arc basin if

subduction rate is faster than forward motion of

overriding plate.

77

2. Oceanic-Continental Boundary - Oceanic plate is

dense and subducts under the Lighter continental

plate. Produces deep ocean trench at the edge of the

continent. About half the oceanic sediment descends

with the subducting plate; the other half is piled up

against the continent. Subducting plate and sediments

partially melt, producing andesitic or granitic magma.

Produces volcanic mountain chains on continents called

volcanic arcs and batholiths. Part of the oceanic plate

can be broken off and thrust up onto the continent

during subduction (obduction). Obduction can expose

very deep rocks (oceanic crust, sea floor sediment, and

mantle material) at the surface. Characterized by

shallow to intermediate focus earthquakes with rare

deep focus earthquakes.

78

3. Continental-Continental Boundary - Continental

crust cannot subduct, so continental rocks are piled up,

folded, and fractured into very high complex mountain

systems. Characterized by shallow-focus earthquakes,

rare intermediate-focus earthquakes. and practically no

volcanism.

79

o Transform - Plates move laterally past one another. Largely

shear stress with lithosphere being neither created nor

destroyed. Characterized by faults that parallel the direction

of plate movement, shallow-focus earthquakes, intensely

shattered rock, and no volcanic activity. Shearing motion can

produce both compressional stress and tensional stress

where a fault bends. Transform faults occur on land, connect

segments of the oceanic ridge, and provide the mechanism

by which crust can be carried to subduction zones.

80

Types of Faults

A fault is a fracture or zone of fractures between two blocks of

rock. Faults allow the blocks to move relative to each other. This

movement may occur rapidly, in the form of an earthquake - or

may occur slowly, in the form of creep. Faults may range in length

from a few millimeters to thousands of kilometers. Most faults

produce repeated displacements over geologic time. During an

earthquake, the rock on one side of the fault suddenly slips with

respect to the other. The fault surface can be horizontal or vertical

or some arbitrary angle in between.

Earth scientists use the angle of the fault with respect to the

surface (known as the dip) and the direction of slip along the fault

to classify faults. Faults that move along the direction of the dip

plane are dip-slip faults and described as either normal or reverse,

depending on their motion. Faults that move horizontally are

known as strike-slip faults and are classified as either right-lateral

or left-lateral. Faults that show both dip-slip and strike-slip motion

are known as oblique-slip fault.

81

slip fault in which the block above the -is a dip A normal faultfault has moved downward relative to the block below. This type of faulting occurs in response to extension and is often observed in the Western United States Basin and Range Province and along

oceanic ridge systems.

82

slip fault in which the upper block, above -is a dip A thrust faultthe fault plane, moves up and over the lower block. This type of faulting is common in areas of compression, such as regions where one plate is being subducted under another as in Japan and along the Washington coast. When the dip angle is shallow, a reverse

fault is often described as a thrust fault.

83

lt on which the two blocks slide past is a fau slip fault-A strikeone another. These faults are identified as either right-lateral or left lateral depending on whether the displacement of the far block is to the right or the left when viewed from either side. The San

Andreas Fault in California is an example of a right lateral fault.

84

CAUSES OF EARTHQUAKES

An earthquake is a sudden shuddering or trembling of the earth

produced by shock waves or vibrations passing through it. Earthquakes

occur in regions of the earth that are undergoing deformation. Energy is

stored in the form of elastic strain as the region is deformed. This

process continues until the accumulated strain exceeds the strength of

the rock, and then fracture or faulting occurs. The opposite sides of the

fault rebound to a new equilibrium position, and the energy is released

in the vibrations of seismic waves and in heating and crushing of the

) focus, hypocenter( rock. Rock fracturing usually start from a point

close to one edge of the fault plane and propagates along the plane with

a typical velocity of some 3 Km/sec. The vertical projection of the

.epicenterhypocenter onto the earth's surface is called the

85

Types of earthquakes

There are many different types of earthquakes: tectonic, volcanic, and explosion. The type of earthquake depends on the region where it

occurs and the geological make-up of that region.

1. tectonic earthquakes. These occur when rocks in

the earth's crust break due to geological forces created

by movement of tectonic plates.

2. volcanic earthquakes, occur in conjunction with

volcanic activity.

3. Collapse earthquakes are small earthquakes in

underground caverns and mines.

4. Explosion earthquakes result from the explosion of

nuclear and chemical devices.

EARTHQUAKES , WHY AND WHERE DO THEY OCCUR ?

It has long been recognized that earthquakes are not evenly distributed

over the earth. The eventual correlation of the earthquake pattern with

volution of the the earth's major surface features was a key to the e

. This is the most recent and broadly satisfying theory tectonics plate

explanation theory of the majority of earthquakes. The basic idea is that

the earth's outermost part ( Lithosphere ) consists of several large and

fairly stable slabs of solid and relatively rigid rock called plates. Each

plate extends to a depth of about 80 Km .

There are two major belts along which most of the world's

). earthquakes Interplateearthquakes occur (

the seismic : A large part ( 80 % ) of belt pacific -circum The1.

energy released by all earthquakes is released along this belt. This

includes the western coasts of South and North America , Japan,

Philippines, and a strip through the East Indies and New Zealand.

86

A high energy : belt ) European - Asiatic ( Alpide The2.

concentration ( 10 % ) can also be seen along this belt. It extends

from the Pacific belt in New Guinea through Summatra and Indonesia,

the Himalayas, and mountains and faults of the Middle East , the Alps ,

and into the Atlantic Ocean far as the Azores.

Sporadically, earthquakes also occur at rather large distances from the

, earthquakes Intraplate respective plate margins . These so called

show a diffuse geographical distribution and there origin is still poorly

understood. It can be large and because of there unexpectedness and

infrequency can cause major disasters.

87

According to the focal depth, earthquakes are classified into one of the three categories :

: have their foci at a depth between earthquakes focus-Shallow1.

0 and 70 Km. and take place at oceanic ridges and transform faults as

well as at subduction zones.

: focal depth between 71 and earthquake focus-Intermediate2.

300 Km.

: focal depth greater than 300 Km focus earthquakes-3. Deep

Mohothe crust. At depth beneath the Most earthquakes originate within

(Crust-Mantle boundary), the number falls abruptly and dies away to

zero at a depth of about 700 Km. Earthquakes along ridges usually occur

at a depth of about 10 Km or less and are of moderate size. Transform

faults generate large shocks at depth down to about 20 Km. The largest

earthquakes occur along subduction zones.

Locating the Epicenter of an Earthquake and Measuring its Magnitude.

P waves and S waves travel at different velocities. The first P wave will

arrive at a seismic station before the first S wave. By using the

difference in their arrival times you can determine the distance between

the epicenter of any Earthquake and a seismic station using the

conversion table at the bottom of the page. Once you have determined

that distance, you can use it as the radius of a circle and can draw a

circle around the seismic station. You need two other seismic stations

doing the same thing. Where the three circles intersect is approximately

where the epicenter of the Earthquake is.

88

To determine the magnitude of an Earthquake you simply measure the greatest amplitude of the first S wave and use the conversion table below to find the Earthquake's magnitude.

89

Below is the conversion chart used to determine both the distance of the epicenter of an Earthquake and the magnitude of the earthquake.

90

SCALES OF EARTHQUAKES

Two basically different scales are used to describe the size or strength of

an earthquake and its effect :

1. Intensity : earthquake intensity represents the degree of shaking at

a particular location on the earth's surface. It indicates the local effect or

damage of the earthquake upon people, animals, buildings and objects

in the immediate environment. The intensity diminishes generally with

increasing distance from the epicenter.

One of the most widely used scales for intensity is the Modified

Mercalli Scale . The scale has the following values, ranging from I to

XII, usually written in Roman numerals :

I. Not felt

II. Felt by persons at rest

III. Felt indoor. Hanging objects swing

IV. Vibration like passing of heavy trucks. Windows rattle.

V. Felt outdoors. Sleepers awakened.

VI. Felt by all Persons walk unsteadily. Glassware broken.

VII. Difficult to stand. Hanging objects quiver.

VIII. Twisting,fall of chimneys,factory stacks,towers.

IX. General panic.Undergroundpipes broken.Frames racked.

X. Most masonry and frame structures destroyed.

XI. Rails bent greatly.Underground pipes out of surface.

XII. Damage nearly total. Objects thrown into the air.

2. Magnitude : The magnitude of an earthquake is an expression of

the actual original force or energy of the earthquake at its moment of

creation. It is measured directly by instruments, unlike the subjective

measurement of intensity.

The Richter scale is a standard for expressing magnitude of

earthquakes. Magnitude is defined as the logarithm to the base 10 of

the amplitude of the largest ground motion traced by a standard type

seismograph placed 100 Km from the earthquake's epicenter.

The Richter scale of magnitude runs from 0 through 8.9 , although

there is no lower limit or upper limit. Each unit representing a ten-fold

91

increase in amplitude of the measured waves and nearly a 30-fold

increase in energy. An earthquake of magnitude 1 can only detected by

a seismograph. The weakest earthquakes noticed by people are usually

around magnitude 2. Houses and buildings are damaged at magnitude

5. Earthquakes with a magnitude above 6 are capable of producing

serious damage. An earthquake with a magnitude of 8 and above is

considered a great earthquake.

All the magnitude scales are of the form :

M = log ( A / T ) + q ( d , h ) + a

Where :

M is the magnitude

A is the maximum amplitude of the wave

T is the period of the wave

q is a function correcting for the decrease of amplitude with

distance from the epicenter and focal depth ( h )

d is the epicentral distance

a is an empirical constant

When the surface - wave magnitude ( Ms ) and body-wave magnitude (

mb ) are calculated for an earthquake, they do not usually have the

same value.

mb = 2.94 + 0.55 Ms

Structural damage is related to ground acceleration, although building

respond differently to seismic waves of different periods. Intensity ( I )

is calibrated in terms of ground acceleration ( a ) by an approximate

relationship

92

log a = ( I / 3 ) - 2.5

The approximate relationship between the magnitude and intensity has

been estimated according to the following relationship :

M = 2 I / 3 + 1.7 log h - 1.4

Magnitude (Richter Scale )

Intensity (Mecalli Scale)

Damage Description

4 5.5 Widely felt, plaster cracked

5 7 Strong vibration, weak buildings and chimneys damaged

6 8.5 Ordinary buildings badly damaged

7 10 Well-built buildings destroyed

8 11.5 Specially designed buildings damaged

9 12 Widespread destruction

An earthquake of Richter magnitude 5.5 turns out to have an energy of

about 10 ergs. The relation between energy and magnitude is :

log E = 5.24 + 1.44 Ms

E : is the total energy measured in joules

Ms : is the surface-wave magnitude.

An increase in magnitude Ms of 1 unit increases the amount of seismic

energy E released by a factor of about 30. In comparison , the

Hiroshima atomic bomb was approximately equivalent in terms of

energy to an earthquake of magnitude 5.3. A one megaton nuclear

explosion would release about the same amount of energy as an

earthquake of magnitude 6.5.

93

CHAPTER 5

ELECTRICAL METHOD

- Electrical properties of rocks

- Apparent & True resistivity

- Electrode configurations

- Electrical soundings & Profiling

- Applications in groundwater exploration

Problem Set - 4

94

SMETHOD ELECTRICAL

ELECTRICAL PROPERTIES OF ROCKS :

Resistivity (or conductivity), which governs the amount of current that passes when a potential difference is created.

Electrochemical activity or polarizability, the response of certain

minerals to electrolytes in the ground, the bases for SP and IP. Dielectric constant or permittivity. A measure of the capacity of a

material to store charge when an electric field is applied . It measure the polarizability of a material in an electric field = 1 + 4 π X

X : electrical susceptibility . Electrical methods utilize direct current or Low frequency alternating current to investigate electrical properties of the subsurface. Electromagnetic methods use alternating electromagnetic field of high frequencies. Two properties are of primary concern in the Application of electrical methods. (1) The ability of Rocks to conduct an electrical current. (2) The polarization which occurs when an electrical current is passed

through them (IP).

Resistivity

For a uniform wire or cube, resistance is proportional to length and inversely proportional to cross-sectional area. Resistivity is related to resistance but it not identical to it. The resistance R depends an length, Area and properties of the material which we term resistivity (ohm.m) .

Constant of proportionality is called Resistivity :

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Resistivity is the fundamental physical property of the metal in the wire

Resistivity is measured in ohm-m

Conductivity meter (S/m), equivalent to ohm-1m-1.

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Classification of Materials according to Resistivities Values

a) Materials which lack pore spaces will show high resistivity such as :

- massive limestone - most igneous and metamorphic (granite, basalt)

- Materials whose pore space lacks water will show

high resistivity such as : - dry sand and gravel , Ice .

b) Materials whose connate water is clean (free from salinity )

will show high resistivity such as : - clean sand or gravel , even if water saturated.

c) most other materials will show medium or low resistivity,

especially if clay is present such as : - clay soil - weathered rock.

The presence of clay minerals tends to decrease the Resistivity because

1 ) The clay minerals can combine with water .

2) The clay minerals can absorb cations in an exchangeable state on

the surface.

3) The clay minerals tend to ionize and contribute to the supply of

free ions.

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Factors which control the Resistivity

(1) Geologic Age (2) Salinity. (3) Free-ion content of the connate water. (4) Interconnection of the pore spaces (Permeability). (5) Temperature. (6) Porosity. (7) Pressure (8) Depth

Archie’s Law

Empirical relationship defining bulk resistivity of a saturated porous rock. In sedimentary rocks, resistivity of pore fluid is probably single most important factor controlling resistivity of whole rock.

Archie (1942) developed empirical formula for effective resistivity of rock:

ρ0 = bulk rock resistivity ρw = pore-water resistivity a = empirical constant (0.6 < a < 1) m = cementation factor (1.3 poor, unconsolidated) < m < 2.2 (good, cemented or crystalline) φ = fractional porosity (vol liq. / vol rock)

Formation Factor: Effects of Partial Saturation:

Sw is the volumetric saturation. n is the saturation coefficient (1.5 < n < 2.5).

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Archie’s Law ignores the effect of pore geometry, but is a reasonable approximation in many sedimentary rocks

Current Flow in A Homogeneous Earth

1. Point current Source :

If we define a very thin shell of thickness dr we can define the potential different dv dv = I ( R ) = I ( ρ L / A ) = I ( ρ dr / 2π r2 ) To determine V a t a point . We integrate the above eq. over its distance D to to infinity : V = I ρ / 2π D C: current density per unit of cross sectional area :

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2. Two current electrodes

To determine the current flow in a homogeneous, isotropic earth when we have two current electrodes. The current must flow from the positive (source ) to the resistive ( sink ). The effect of the source at C1 (+) and the sink at C2 (-) Vp1 = i ρ / 2π r1 + ( - iρ / 2π r2 )

} 0.5]2 + Z 2x ) -1 / [ (d/2 - 0.5]2 + Z 2= iρ / 2π { 1/ [ (d/2 + x ) 1Vp

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3. Two potential Electrodes

Vp1 = i ρ / 2π r1 - iρ / 2π r2 Vp2= i ρ / 2π r3 - iρ / 2π r4 Δ V = Vp1 –Vp2 = i ρ / 2π ( 1/r1 – 1 / r2 – 1 / r3 + 1 / r4 )

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ELECTRODE CONFIGURATIONS

The value of the apparent resistivity depends on the geometry of the electrode array used (K factor)

1- Wenner Arrangement Named after wenner (1916) . The four electrodes A , M , N , B are equally spaced along a straight line. The distance between adjacent electrode is called “a” spacing . So AM=MN=NB= ⅓ AB = a.

Ρa= 2 π a V / I

The wenner array is widely used in the western Hemisphere. This array is sensitive to horizontal variations.

2) Schlumberger Arrangement . This array is the most widely used in the electrical prospecting . Four electrodes are placed along a straight line in the same order AMNB , but with AB ≥ 5 MN

This array is less sensitive to lateral variations and faster to use as only the current electrodes are moved. 3. Dipole – Dipole Array .

The use of the dipole-dipole arrays has become common since the 1950’s , Particularly in Russia. In a dipole-dipole, the distance between the current electrode A and B (current dipole) and the distance between the potential electrodes M and N (measuring

MN

MNAB

I

Va

22

22

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dipole) are significantly smaller than the distance r , between the centers of the two dipoles.

ρa = π [ ( r2 / a ) – r ] v/i

Or . if the separations a and b are equal and the distance between the centers is (n+1) a then

ρa = n (n+1) (n+2) . π a. v/i

This array is used for deep penetration ≈ 1 km.

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REFRACTION OF ELECTRICAL RESISTIVITY

A. Distortion of Current flow

At the boundary between two media of different resistivities the potential remains continuous and the current lines are refracted according to the law of tangents. tan Ө1 / tan Ө2 = P2 / P1

Ρ1 tan Ө1 = Ρ2 tan Ө2 If ρ2 < p1 , The current lines will be refracted away from the Normal. The line of flow are moved downward because the lower resistivity below the interface results in an easier path for the current within the deeper zone. B. Distortion of Potential Consider a source of current I at the point S in the first layers P1 of Semi infinite extent. The potential at any point P would be that from S plus the amount reflected by the layer P2 as if the reflected amount were coming from the image S/

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) ] 2) + ( K / r1/ 2π [ (1 / r 1ρ (P) = i 1V

1+ ρ 2/ ρ 1ρ – 2K = Reflection coefficient = ρ

In the case where P lies in the second medium ρ2, Then transmitting light coming from S. Since only 1 – K is transmitted through the boundary. The Potential in the second medium is

V2(P) = I ρ2/ 2π [ (1 / r1) – (K / r1) ] Continuity of the potential requires that the boundary where r1 = r2 , V1(p) must be equal to V2 ( P). At the interface r1 = r2 , V1= V2

k is electrical reflection coefficient and used in interpretation

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The value of the dimming factor , K always lies between ± 1 If the second layer is a pure insulator ( ρ2 = ω ) then K = + 1 If the second layer is a perfect conductor ( ρ2 = O ) then K = - 1 When ρ1 = ρ2 then No electrical boundary Exists and K =

O .

SURVEY DESIGN Two categories of field techniques exist for conventional resistivity

analysis of the subsurface. These techniques are vertical electric

sounding (VES), and Horizontal Electrical Profiling (HEP).

1- Vertical Electrical Sounding (VES) .

The object of VES is to deduce the variation of resistivity with

depth below a given point on the ground surface and to correlate

it with the available geological information in order to infer the

depths and resistivities of the layers present.

2- Horizontal Electrical profiling (HEP) .

The object of HEP is to detect lateral variations in the resistivity of

the ground, such as lithological changes, near- surface faults……

.

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Multiple Horizontal Interfaces

For Three layers resistivities in two interface case , four possible curve types exist. 1- Q – type ρ1> ρ2> ρ3 2- H – Type ρ1> ρ2< ρ3 3- K – Type ρ1< ρ2> ρ3 4- A – Type ρ1< ρ2< ρ3

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Applications of Resistivity Techniques

1. Bedrock Depth Determination

Both VES and CST are useful in determining bedrock depth. Bedrock

usually more resistive than overburden. HEP profiling with Wenner array

at 10 m spacing and 10 m station interval used to map bedrock highs.

2. Location of Permafrost

Permafrost represents significant difficulty to construction projects due

to excavation problems and thawing after construction.

Ice has high resistivity of 1-120 ohm-m

3. Landfill Mapping

Resistivity increasingly used to investigate landfills:

Leachates often conductive due to dissolved salts

Landfills can be resistive or conductive, depends on contents

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Limitations of Resistivity Interpretation

1- Principle of Equivalence.

If we consider three-lager curves of K (ρ1< ρ2> ρ3 ) or Q type

(ρ1> ρ2> ρ3) we find the possible range of values for the

product T2= ρ2 h2 Turns out to be much smaller. This is called

T-equivalence. H = thickness, T : Transverse resistance it

implies that we can determine T2 more reliably than ρ2 and h2

separately. If we can estimate either ρ2 or h2 independently we

can narrow the ambiguity. Equivalence: several models produce

the same results. Ambiguity in physics of 1D interpretation such

that different layered models basically yield the same response.

Different Scenarios: Conductive layers between two

resistors, where lateral conductance (σh) is the same.

Resistive layer between two conductors with same transverse

resistance (ρh).

2- Principle of Suppression.

This states that a thin layer may sometimes not be detectable on

the field graph within the errors of field measurements. The thin

layer will then be averaged into on overlying or underlying layer in

the interpretation. Thin layers of small resistivity contrast with

respect to background will be missed. Thin layers of greater

resistivity contrast will be detectable, but equivalence limits

resolution of boundary depths, etc. The detectibility of a layer of

given resistivity depends on its relative thickness which is defined

as the ratio of Thickness/Depth.

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Comparison of Wenner and Schlumberger

(1) In Sch. MN ≤ 1/5 AB Wenner MN = 1/3 AB (2) In Sch. Sounding, MN are moved only occasionally.

In Wenner Soundings, MN and AB are moved after each measurement.

(3) The manpower and time required for making Schlumberger

soundings are less than that required for Wenner soundings. (4) Stray currents that are measured with long spreads effect

measurements with Wenner more easily than Sch. (5) The effect of lateral variations in resistivity are recognized and

corrected more easily on Schlumberger than Wenner. (6) Sch. Sounding is discontinuous resulting from enlarging MN.

Disadvantages of Wenner Array

1. All electrodes must be moved for each reading 2. Required more field time 3. More sensitive to local and near surface lateral variations 4. Interpretations are limited to simple, horizontally layered structures

Advantages of Schlumberger Array

1. Less sensitive to lateral variations in resistivity 2. Slightly faster in field operation 3. Small corrections to the field data

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Disadvantages of Schlumberger Array

1. Interpretations are limited to simple, horizontally layered structures 2. For large current electrodes spacing, very sensitive voltmeters are required.

Advantages of Resistivity Methods

1. Flexible 2. Relatively rapid. Field time increases with depth 3. Minimal field expenses other than personnel 4. Equipment is light and portable 5. Qualitative interpretation is straightforward 6. Respond to different material properties than do seismic and other methods, specifically to the water content and water salinity

Disadvantages of Resistivity Methods

1- Interpretations are ambiguous, consequently, independent

geophysical and geological controls are necessary to discriminate between valid alternative interpretation of the resistivity data ( Principles of Suppression & Equivalence)

2- Interpretation is limited to simple structural configurations.

3- Topography and the effects of near surface resistivity variations

can mask the effects of deeper variations.

4- The depth of penetration of the method is limited by the maximum electrical power that can be introduced into the ground and by the practical difficulties of laying out long length of cable. The practical depth limit of most surveys is about 1 Km.

5. Accuracy of depth determination is substantially lower than with seismic methods or with drilling.

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Problem Sets

1. Copper has ρ =1.7 X 10-8 ohm.m. What is the resistance of 20 m of copper with a cross-sectional radius of 0.005 m .

2. Construct the current-flow lines beneath the interface in (a) and (b).

3. Assume a homogeneous medium of resistivity 120 ohm-m. Using the wenner electrode system with a 60-m spacing, assume a current of 0.628 ampere. What is the measured potential differ-ence? What will be the potential difference if we place the sink (negative-current electrode) at infinity?

4. Why are the electrical methods of exploration particularly suited to hydrogeological investigations? Describe other geophysical methods which could be used in this context, stating the reasons why they are applicable.

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CHAPTER 6

GRAVITY METHOD

- Fundamental principles

- Measurements

- Data reduction

- Interpretation & Applications

Solved Problems

Problem Set - 5

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GRAVITY METHOD

The gravity method is a nondestructive geophysical technique that

measures differences in the earth’s gravitational field at specific

locations. It has found numerous applications in engineering and

environmental studies including locating voids and karst features, buried

stream valleys, water table levels and the determination of soil layer

thickness. The success of the gravity method depends on the different

earth materials having different bulk densities (mass) that produce

variations in the measured gravitational field. These variations can then

be interpreted by a variety of analytical and computers methods to

determine the depth, geometry and density the causes the gravity field

variations.

Gravity data in engineering and environmental applications should be

collected in a grid or along a profile with stations spacing 5 meters or

less. In addition, gravity station elevations must be determined to within

0.2 meters. Using the highly precise locations and elevations plus all

other quantifiable disturbing effects, the data are processed to remove

all these predictable effects. The most commonly used processed data

are known as Bouguer gravity anomalies, measured in mGal.

The gravity method can be a relatively easy geophysical technique to

perform and interpret. It requires only simple but precise data

processing, and for detailed studies the determination of a station’s

elevation is the most difficult and time-consuming aspect. The technique

has good depth penetration when compared to ground penetrating

radar, high frequency electromagnetics and DC-resistivity techniques

and is not affected by the high conductivity values of near-surface clay

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rich soils. Additionally, lateral boundaries of subsurface features can be

easily obtained especially through the measurement of the derivatives of

the gravitational field.

The main drawback is the ambiguity of the interpretation of the

anomalies. This means that a given gravity anomaly can be caused by

numerous source bodies. An accurate determination of the source

usually requires outside geophysical or geological information.

Geophysical interpretations from gravity surveys are based on the

mutual attraction experienced between two masses* as first expressed

by Isaac Newton. Newton's law of gravitation states that the mutual

attractive force between two point masses**, m1 and m2, is

proportional to one over the square of the distance between them. The

constant of proportionality is usually specified as G, the gravitational

constant. Thus, the law of gravitation

where F is the force of attraction, G is the gravitational constant

( G = 6.67 x 10-11 m3 kg-1 s-2 ) and r is the distance between the two

masses, m1 and m2.

Mass is formally defined as the proportionality constant relating the

force applied to a body and the acceleration the body undergoes as

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given by Newton's second law, usually written as F=ma. Therefore,

mass is given as m=F/a and has the units of force over acceleration.

Gravitational Acceleration

When making measurements of the earth's gravity, we usually don't

measure the gravitational force, F. Rather, we measure the gravitational

acceleration, g. The gravitational acceleration is the time rate of change

of a body's speed under the influence of the gravitational force. That is,

if you drop a rock off a cliff, it not only falls, but its speed increases as it

falls. In addition to defining the law of mutual attraction between

masses, Newton also defined the relationship between a force and an

acceleration.

Newton's second law states that force is proportional to acceleration.

The constant of proportionality is the mass of the object. Combining

Newton's second law with his law of mutual attraction, the gravitational

acceleration on the mass m2 can be shown to be equal to the mass of

attracting object, m1, over the squared distance between the center of

the two masses, r.

If an object such as a ball is dropped, it falls under the influence of

gravity in such a way that its speed increases constantly with time. That

is, the object accelerates as it falls with constant acceleration. At sea

level, the rate of acceleration is about 9.8 meters per second squared.

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In gravity surveying, we will measure variations in the acceleration due

to the earth's gravity. Variations in this acceleration can be caused by

variations in subsurface geology. Acceleration variations due to geology,

however, tend to be much smaller than 9.8 meters per second squared.

Thus, a meter per second squared is an inconvenient system of units to

use when discussing gravity surveys.

The units typically used in describing the gravitational acceleration

variations observed in exploration gravity surveys are specified in

milliGals. A Gal is defined as a cm / sec.2 (1 mGal=10-3 Gal) and

microgal (1μGal = 10-6 Gals ).

Thus, the Earth's gravitational acceleration is approximately 980 Gals.

The Gal is named after Galileo Galilei. The milliGal (mgal) is 0.001 Gal.

In milliGals, the Earth's gravitational acceleration is approximately

980,000.

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Gravity Measurements The instrument used to measure gravity is called a gravimeter. Absolute gravity

This technique makes measurements of the total gravity field at a

site. There are a number of types of instruments, including free-fall

devices, the reversible pendulum, and superconducting gravimeters. The

equipment is very expensive and bulky. Lengthy observation times (24+

hrs) are required to obtain accurate readings (0.001- 0.01 mgal).

Relative gravity

In general, for interpreting gravity data, only the relative gravitational

acceleration is required. Therefore, we usually don’t need to know the

absolute gravity at every station, just how gravity changes between

stations. The relative gravity readings can be converted into absolute

gravity if one of the survey sites is chosen to be a place where the

absolute gravity was measured previously.

a) Portable pendulum:

- based on the idea that the period of a pendulum (time taken for

the pendulum to swing back and forth) is given by:

where L is the pendulum length and g is the gravity.

- measure the period (T1) at one location and then move the

pendulum to another location and measure the period (T2). The

change in period (T2- T1) is proportional to the change in gravity

between the two locations.

- accuracy of 0.25 mgal

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Factors Affecting Gravitational Acceleration Factors can be subdivided into two categories: those that give rise to

temporal variations and those that give rise to spatial variations in the

gravitational acceleration.

A. Temporal Based Variations - These are changes in the

observed acceleration that are time dependent. In other words,

these factors cause variations in acceleration that would be

observed even if we didn't move our gravimeter.

Instrument Drift - Changes in the observed acceleration caused by

changes in the response of the gravimeter over time.

Tidal Affects - Changes in the observed acceleration caused by the

gravitational attraction of the sun and moon.

B. Spatial Based Variations - These are changes in the observed

acceleration that are space dependent. That is, these change the

gravitational acceleration from place to place, just like the geologic

affects, but they are not related to geology.

Latitude Variations - Changes in the observed acceleration caused by

the ellipsoidal shape and the rotation of the earth.

Elevation Variations - Changes in the observed acceleration caused

by differences in the elevations of the observation points.

Bouguer Effects - Changes in the observed acceleration caused by the

extra mass underlying observation points at higher elevations.

Topographic Effects - Changes in the observed acceleration related to

topography near the observation point.

Latitude Variations:

Two features of the earth's large-scale structure and dynamics affect our

gravity observations: its shape and its rotation.

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Although the difference in earth radii measured at the poles and at the

equator is only 22 km (this value represents a change in earth radius of

only 0.3%), this, in conjunction with the earth's rotation, can produce a

measurable change in the gravitational acceleration with latitude.

Because this produces a spatially varying change in the gravitational

acceleration, it is possible to confuse this change with a change

produced by local geologic structure. Fortunately, it is a relatively simple

matter to correct our gravitational observations for the change in

acceleration produced by the earth's elliptical shape and rotation.

To first order*, the elliptical shape of the earth causes the gravitational

acceleration to vary with latitude because the distance between the

gravimeter and the earth's center varies with latitude. The magnitude of

the gravitational acceleration changes as one over the distance from the

center of mass of the earth to the gravimeter squared. Thus,

qualitatively, we would expect the gravitational acceleration to be

smaller at the equator than at the poles, because the surface of the

earth is farther from the earth's center at the equator than it is at the

poles.

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The mathematical formula used to predict the components of the

gravitational acceleration produced by the earth's shape and rotation is

called the Geodetic Reference Formula of 1967. The predicted gravity is

called the normal gravity ( gn ).

How large is this correction to our observed gravitational acceleration?

And, because we need to know the latitudes of our observation points to

make this correction, how accurately do we need to know locations? At

a latitude of 45 degrees, the gravitational acceleration varies

approximately 0.813 mgals per kilometer. Thus, to achieve an accuracy

of 0.01 mgals, we need to know the north-south location of our gravity

stations to about 12 meters.

At any latitude gn = 0.812 sin 2φ mgal/m

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Observed Gravity (gobs) - Gravity readings observed at each gravity

station after corrections have been applied for instrument drift and tides.

Latitude Correction (gn) - Correction subtracted from gobs that

accounts for the earth's elliptical shape and rotation. The gravity value

that would be observed if the earth were a perfect (no geologic or

topographic complexities), rotating ellipsoid is referred to as the normal

gravity.

Free Air Corrected Gravity (gfa) - The Free-Air correction accounts for

gravity variations caused by elevation differences in the observation

locations. The form of the Free-Air gravity anomaly, gfa, is given by;

gfa = gobs - gn + 0.3086h (mgal)

where h is the elevation at which the gravity station is above the

elevation datum chosen for the survey (this is usually sea level).

Bouguer Slab Corrected Gravity (gb) - The Bouguer correction is a

first-order correction to account for the excess mass underlying

observation points located at elevations higher than the elevation

datum. Conversely, it accounts for a mass deficiency at observations

points located below the elevation datum. The form of the Bouguer

gravity anomaly, gb, is given by;

gb = gobs - gn + 0.3086h - 0.04193rh (mgal)

where r is the average density of the rocks underlying the survey area.

Terrain Corrected Bouguer Gravity (gt) - The Terrain correction

accounts for variations in the observed gravitational acceleration caused

by variations in topography near each observation point. The terrain

correction is positive regardless of whether the local topography consists

of a mountain or a valley. The form of the Terrain corrected, Bouguer

gravity anomaly, gt, is given by;

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gt = gobs - gn + 0.3086h - 0.04193r + TC (mgal)

where TC is the value of the computed Terrain correction. Assuming

these corrections have accurately accounted for the variations in

gravitational acceleration they were intended to account for, any

remaining variations in the gravitational acceleration associated with the

Terrain Corrected Bouguer Gravity, gt, can now be assumed to be

caused by geologic structure.

FREE AIR AND BOUGUER ANOMALIES

A. Free Air anomaly

The figure below shows three gravity sites in an area with a hill and a

valley.

As you go from site A to site B, you climb a hill that is 100 m high. The

corresponding change in gravity is: Δg = 0.3086 x 100 = 30.86 mgal

. The gravity at the top of the hill will be 30.86 mgal less than the

gravity at the bottom because you have moved further from the centre

of the Earth.

This variation in gravity must be removed from your data. The

correction for elevation is called the Free Air Correction. To apply this,

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it is necessary to define a reference level for the survey. Any reference

level can be chosen:

- for surveys in coastal areas, sea level is often chosen as the reference

- for a survey far away from the coast, the average elevation of the

survey area could be used.

- in the figure, the elevation of Site A was chosen. The Free Air

Correction is written as: CFA = 0.3086 Δh, where Δh is the difference

in elevation between the site and the reference level

• If the site is above the reference level (e.g., Site B), CFA is added to

the observed gravity value.

• If the site is below the reference level (e.g., Site C), CFA is

subtracted from the observed gravity value. The resulting gravity value

is called the free air anomaly. gF = gobs - g + CF

B. Bouguer Anomaly

Consider Sites A and B. The Free Air correction will correct the gravity

observed at B for the 100 m difference in elevation. However, there is

still a difference in the amount of mass below each station. The gravity

at Site B will be affected by the gravitational pull of the 100 m thickness

of the material between it and the reference level. This “excess” gravity

has to be removed in order to compare the gravity at A and B.

To first order, the difference in gravity between Site A and Site B can be

approximated by an infinite slab of uniform density and thickness. The

gravitational attraction of this layer is: g = 2πGρΔh , where Δh is the

thickness and ρ is the density of the material . The correction for the

difference in mass due to a difference elevation (Δh) is called the

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Bouguer correction (CB): C = 2πGρΔh = B 0.00004193 ρ Δh (CB in

mgal). The Bouguer correction at Site B would be: 0.1119 Δh =

0.1119×100 m = 11.2 mgal.

This value must be subtracted – we want to take away the effect of

the hill. Conversely, after the gravity data at site C have been corrected

for elevation (CFA), they will be “too low”, because they were made at a

lower elevation and thus there was less mass below the station. In this

case, the Bouguer correction will add the “missing” mass to the original

gravity measurement. The resulting gravity value is the Bouguer

anomaly,

gB = gobs - g + CF - CB + CT

this is the gravity anomaly due to local geology.

Generally, measurement above reference level Add Free Air Subtract

Bouguer correction correction. Measurement below reference level

Subtract Free Air Add Bouguer correction.

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Applications of the Gravity Method

Determining Shape of the earth ( Geodesy )

Detection of subsurface voids including caves, mine shafts

Determining the amount of subsidence in surface collapse features

over time

Determination of soil and glacier sediment thickness (bedrock

topography)

Location of buried sediment valleys

Determination of groundwater volume and changes in water table

levels over time in alluvial basins

Mapping the volume, lateral and vertical extent of landfills

Mapping steeply dipping contacts including faults

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SOLVED PROBLEMS IN GRAVITY

Problem 1:

Given : Observed gravity at base 980.30045 Gals Observed gravity at station relative to base + 5.65 mGal Theoretical gravity at sea level at latitude of station 980.30212 Gals Elevation of station 100 m above sea level Density of rock above sea level 2.0 g/cc Terrain effect 0.15 mGals Compute : Bouguer gravity anomaly Free air anomaly gB = gobs - g + CF - CB + CT = (980300.54 + 5.65) - (980302.12 + (0.3086 x 100) - (0.0419 x 100 x 2) + 0.15 g = 980306.19 - 980302.12 + 30.86 - 8.38 + 0.15 gB = 26.55 mGal

gF = gobs - g + CF

= 34.9 mGal

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Problem 2 : Given : Observed gravity at base 980.30045 Gals Observed gravity at station relative to base + 5.65 mGal Theoretical gravity at sea level at latitude of station 980.30212 Gals Elevation of station 100 m below sea level Density of rock above sea level 2.0 g/cc Terrain effect 0.15 mGals Compute : 1 - Free air anomaly 2 - Bouguer gravity anomaly gF = gobs - g + CF

= 980306.19 – 980302.12 + (0.3086 x -100) = - 26.79 mGal gB = gobs - g + CF - CB + CT

= 980306.19 - 980302.12 + (0.3086 x -100) - (0.0419 x 2.0 x - 100) + 0.15 = - 18.26 mGal

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Problem 3 : Given : Observed gravity relative to base + 30 mGal Elevation of station 150 m above base Station is 1000 m north of base Latitude effect is 0.00025 mGal/m Density is 1.8 g/cc Terrain effect is 0.05 mGal Compute : Free-air and Bouguer Anomalies gF = gobs - g + CF

= 30 - (0.00025 x 1000) + 0.3086 x 150) = 30 - 0.25 + 46.29 = 76.04 mGal gB = gobs - g + CF - CB + CT

= 76.04 - (0.0419 x 1.8 x 150) + 0.05 = 76.04 - 11.313 + 0.05 = 64.777 mGal

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Problem 4 : Given: Observed gravity relative to base - 12.5 mGal Elevation of station is 100 m below the base Station is 2000 m south of base Latitude effect is 0.00025 mGal/m Density is 1.8 g/cc Terrain effect is 0.1 mGal Compute: 1 - Free air anomaly 2 - Bouguer gravity anomaly gF = gobs - g + CF

= - 12.5 – (0.00025 x - 2000) + (0.3086 x - 100) = - 12.5 + 0.5 - 30.86 = - 42.86 mGal gB = gobs - g + CF - CB + CT

= - 42.86 - (0.0419 x 1.8 x - 100) + 0.1 = - 42.86 +7.542+ 0.1 = - 35.218 mGal

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Problem Sets

Q.1 What is the average gravitational acceleration at the surface of the Earth? Mass of the Earth (ME) = 5.974 × 1024 kg . Average radius of the Earth (r) = 6371 km Q. 2 What is the expected value of gravity at latitude 53.525890 N ? Q.3 Surface gravity at a measuring site is 9.803244 ms-2, the site has latitude 43.1o N and elevation 54 m. Obtain the free air gravity anomalies.

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CHAPTER 7

MAGNETIC METHOD

- Basic concepts

- Description of the magnetic field

- Source of magnetic anomalies

- Measurements

- Interpretation & Applications

Problem Set – 6

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MAGNETIC METHODS

Magnetic methods are one of the most commonly used geophysical

tools. This stems from the fact that magnetic observations are obtained

relatively easily and cheaply and few corrections must be applied to the

observations. Despite these obvious advantages, like the gravitational

methods, interpretations of magnetic observations suffer from a lack of

uniqueness.

Magnetic Monopoles

Charles Coulomb, in 1785, showed that the force of attraction or

repulsion between electrically charged bodies and between magnetic

poles also obey an inverse square law like that derived for gravity by

Newton. The mathematical expression for the magnetic force

experienced between

two magnetic monopoles is given by

where µ is a constant of proportionality known as the magnetic

permeability, p1 and p2 are the strengths of the two magnetic

monopoles, and r is the distance between the two poles. the magnetic

permeability, µ, is a property of the material in which the two

monopoles, p1 and p2, are located. If they are in a vacuum, µ is called

the magnetic permeability of free space. p1 and p2 can be either

positive or negative in sign. If p1 and p2 have the same sign, the force

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between the two monopoles is repulsive. If p1 and p2 have opposite

signs, the force between the two monopoles is attractive.

From Coulomb's expression, we know that force must be given in

Newtons,N, Permeability,mu, is defined to be a unit less constant. The

units of pole strength are defined such that if the force, F, is 1 N and the

two magnetic poles are separated by 1 m, each of the poles has a

strength of 1 Amp - m (Ampere - meters). In this case, the poles are

referred to as unit poles.

The magnetic field strength, H, is defined as the force per unit pole

strength exerted by a magnetic monopole, p1. H is nothing more than

Coulomb's expression divided by p2.

Given the units associated with force, N, and magnetic monopoles, Amp

-m, the units associated with magnetic field strength are Newtons per

Ampere-meter, N / (Amp - m). A N / (Amp - m) is referred to as a tesla

(T), named after the renowned inventor Nikola Tesla

When describing the magnetic field strength of the earth, it is more

common to use units of nanoteslas (nT), where one nanotesla is 1

billionth of a tesla. The average strength of the Earth's magnetic field is

about 50,000 nT. A nanotesla is also commonly referred to as a gamma.

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Magnetic Induction

When a magnetic material, say iron, is placed within a magnetic field, H,

the magnetic material will produce its own magnetization. This

phenomena is called induced magnetization.

In practice, the induced magnetic field will look like it is being created by

a series of magnetic dipoles located within the magnetic material and

oriented parallel to the direction of the inducing field, H.

The strength of the magnetic field induced by the magnetic material due

to the inducing field is called the intensity of magnetization, I.

The intensity of magnetization, I, is related to the strength of the

inducing magnetic field, H, through a constant of proportionality, known

as the magnetic susceptibility.

The magnetic susceptibility ( K) is a unitless constant that is determined

by the physical properties of the magnetic material. It can take on either

positive or negative values. Positive values imply that the induced

magnetic field, I, is in the same direction as the inducing field, H.

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Negative values imply that the induced magnetic field is in the opposite

direction as the inducing field.

Magnetic Susceptibility K is dependent on :

1- The state of magnetization. 2- Intensity of saturation magnetization. 3- Grain size. 4- Internal stress. 5- Shape 6- Mode of dispersion.

The intensity of magnetization I = M / V M = magnetic moment = m L V = Volume m = pole strength L = length Intensity of magnetization ∞ H and has the same direction.

Mechanisms for Induced Magnetization

The nature of magnetization material is in general complex, governed by

atomic properties, and well beyond the scope of this series of notes.

Suffice it to say, there are three types of magnetic materials:

paramagnetic, diamagnetic, and ferromagnetic.

Diamagnetism - Discovered by Michael Faraday in 1846. This form of

magnetism is a fundamental property of all materials and is caused by

the alignment of magnetic moments associated with orbital electrons in

the presence of an external magnetic field. For those elements with no

unpaired electrons in their outer electron shells, this is the only form of

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magnetism observed. The susceptibilities of diamagnetic materials are

relatively small and negative. Quartz and salt are two common

diamagnetic earth materials.

Paramagnetism - This is a form of magnetism associated with

elements that have an odd number of electrons in their outer electron

shells. Paramagnetism is associated with the alignment of electron spin

directions in the presence of an external magnetic field. It can only be

observed at relatively low temperatures. The temperature above which

paramagnetism is no longer observed is called the Curie Temperature.

The susceptibilities of paramagnetic substances are small and positive.

Ferromagnetism - This is a special case of paramagnetism in which

there is an almost perfect alignment of electron spin directions within

large portions of the material referred to as domains.

Like paramagnetism, ferromagnetism is observed only at temperatures

below the Curie temperature. There are three varieties of

ferromagnetism.

Pure Ferromagnetism - The directions of electron spin alignment

within each domain are almost all parallel to the direction of the external

inducing field. Pure ferromagnetic substances have large (approaching

1) positive susceptibilities. Ferrromagnetic minerals do not exist, but

iron, cobalt, and nickel are examples of common ferromagnetic

elements.

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Antiferromagnetism - The directions of electron alignment within

adjacent domains are opposite and the relative abundance of domains

with each spin direction is approximately equal. The observed magnetic

intensity for the material is almost zero. Thus, the susceptibilities of

antiferromagnetic materials are almost zero. Hematite is an

antiferromagnetic material

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Ferromagnetism - Like antiferromagnetic materials, adjacent domains

produce magnetic intensities in opposite directions. The intensities

associated with domains polarized in a direction opposite that of the

external field, however, are weaker. The observed magnetic intensity for

the entire material is in the direction of the inducing field but is much

weaker than that observed for pure ferromagnetic materials. Thus, the

susceptibilities for ferromagnetic materials are small and positive. The

most important magnetic minerals are ferromagnetic and include

magnetite, titanomagnetite, ilmenite, and pyrrhotite.

Remanent Magnetization in Rocks

Remanent field (remains even after external field removed) o thermoremanent o detrital remanent o chemical remanent

Total magnetization (J) = Remanent (Jr) + induced (Ji) intensity of Jr is large in igneous and thermally metamorphosed Rocks. Koenigsberger ratio. Q = Remanent (Jr) / induced (Ji) Q > 1, Jr of sediments is smaller than Ji.

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Magnetic Field Elements

At any point on the Earth's surface, the magnetic field, F*, has some

strength and points in some direction. The following terms are used to

describe the direction of the magnetic field.

Declination - The angle between north and the horizontal projection of

F. This value is measured positive through east and varies from 0 to 360

degrees.

Inclination - The angle between the surface of the earth and F.

Positive inclinations indicate F is pointed downward, negative inclinations

indicate F is pointed upward. Inclination varies from -90 to 90 degrees.

Magnetic Equator - The location around the surface of the Earth

where the Earth's magnetic field has an inclination of zero (the magnetic

field vector F is horizontal). This location does not correspond to the

Earth's rotational equator.

Magnetic Poles - The locations on the surface of the Earth where the

Earth's magnetic field has an inclination of either plus or minus 90

degrees (the magnetic field vector F is vertical). These locations do not

correspond to the Earth's north and south poles.

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The total field F is resolved into its horizontal components H ( x , y ) and

it vertical components Z. The angle which F makes with its horizontal

components H is the inclination (I), and the angle between H and X

(points North) is the declination (D).

F2 = X2 + y2 + Z2 F2 H2 + Z2 H = F cos I Z F sin I X = H cos D Z / H = tan I

Tan I = 2 tan Ø → Latitude

F at North Pole = 60,000 nT F at South Pole = 70,000 nT F at equator = 30.000 nT Fpole = 2 FEquator

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The Earth's Magnetic Field

Ninety percent of the Earth's magnetic field looks like a magnetic field

that would be generated from a dipolar magnetic source located at the

center of the Earth and aligned with the Earth's rotational axis. The

strength of the magnetic field at the poles is about 60,000 nT. The

remaining 10% of the magnetic field can not be explained in terms of

simple dipolar sources.

If the Earth's field were simply dipolar with the axis of the dipole

oriented along the Earth's rotational axis, all declinations would be 0

degrees (the field would always point toward the north).

The magnetic field can be broken into three separate components.

Main Field - This is the largest component of the magnetic field and is

believed to be caused by electrical currents in the Earth's fluid outer

core. For exploration work, this field acts as the inducing magnetic field.

External Magnetic Field - This is a relatively small portion of the

observed magnetic field that is generated from magnetic sources

external to the earth. This field is believed to be produced by

interactions of the Earth's ionosphere with the solar wind. Hence,

temporal variations associated with the external magnetic field are

correlated to solar activity.

Temporal Variations of the Earth's Magnetic Field The magnetic field varies with time. When describing temporal

variations of the magnetic field, it is useful to classify these variations

into one of three types depending on their rate of occurrence and

source. Three temporal variations:

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Secular Variations - These are long-term (changes in the field that

occur over years) variations in the main magnetic field that are

presumably caused by fluid motion in the Earth's Outer Core. Because

these variations occur slowly with respect to the time of completion of a

typical exploration magnetic survey, these variations will not complicate

data reduction efforts.

Diurnal Variations - These are variations in the magnetic field that

occur over the course of a day and are related to variations in the

Earth's external magnetic field. This variation can be on the order of 20

to 30 nT per day and should be accounted for when conducting

exploration magnetic surveys.

Magnetic Storms - Occasionally, magnetic activity in the ionosphere

will abruptly increase. The occurrence of such storms correlates with

enhanced sunspot activity. The magnetic field observed during such

times is highly irregular and unpredictable, having amplitudes as large

as 1000 nT.

Exploration magnetic surveys should not be conducted during magnetic

storms. This is because the variations in the field that they can produce

are large, rapid, and spatially varying. Therefore, it is difficult to correct

for them in acquired data.

Measuring the Earth's Magnetic Field

Magnetometers are highly accurate instruments, allowing the local

magnetic field to be measured to accuracies of 0.002%. The proton

precession, caesium vapour and gradiometer magnetometer systems are

used for commercial applications. The systems operate on broadly

similar principles utilizing proton rich fluids surrounded by an electric

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coil. A momentary current is applied through the coil, which produces a

corresponding magnetic field that temporarily polarizes the protons.

When the current is removed, the protons realign or process into the

orientation of the Earth's magnetic field.

Gradiometers measure the magnetic field gradient rather than total

field strength, which allows the removal of background noise. Magnetic

gradient anomalies generally give a better definition of shallow buried

features such as buried tanks and drums, but are less useful for

investigating large geological features. Unlike EM surveys, the depth

penetration of magnetic surveys is not impeded by high electrical ground

conductivities associated with saline groundwater or high levels of

contamination.

Flux-gate magnetometer

relative instrument

can be used to find vector components, direction of field

portable instruments usually set up to read HZ (vertical

component)

Proton-precession magnetometer

simple, inexpensive, accurate, portable instrument

measures absolute, total value of field

1 nT precision

susceptible to strong magnetic gradients

It shows no appreciable instrument drift with time. One of the important

advantages of the proton precession magnetometer is its ease of use

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and reliability. Sensor orientation need only be set to a high angle with

respect to the Earth's magnetic field. No precise leveling or orientation is

needed. The magnetic field we record with proton precession

magnetometer has two components:

The main magnetic field, or that part of the Earth's magnetic field

generated by deep (outer core) sources. The direction and size of this

component of the magnetic field at some point on the Earth's surface is

represented by the vector labeled Fe in the figure.

The anomalous magnetic field, or that part of the Earth's magnetic

field caused by magnetic induction of crustal rocks or remanent

magnetization of crustal rocks. The direction and size of this component

of the magnetic field is represented by the vector labeled Fa in the

figure. The total magnetic field we record, labeled Ft in the figure, is

nothing more than the sum of Fe and Fa.

Typically, Fe is much larger than Fa, as is shown in the figure (50,000

nT versus 100 nT). If Fe is much larger than Fa, then Ft will point almost

in the same direction as Fe regardless of the direction of Fa.That is

because the anomalous field, Fa, is so much smaller than the main field,

Fe, that the total field, Ft, will be almost parallel to the main field.

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Similarities Between Gravity and Magnetics

Geophysical exploration techniques that employ both gravity and magnetics are passive (measure a naturally occurring field of the earth.

Collectively, the gravity and magnetic methods are often referred to as potential methods.

Identical physical and mathematical representations can be used to understand magnetic and gravitational forces. For example, the fundamental element used to define the gravitational force is the point mass and the fundamental magnetic element is called a magnetic monopole.

The acquisition, reduction, and interpretation of gravity and magnetic observations are very similar.

Both gravity and magnetic vary in time and space and used as reconnaissance tools in exploration.

Differences Between Gravity and Magnetics

The fundamental parameter that controls gravity variations is rock density and the fundamental parameter controlling the magnetic field variations is magnetic susceptibility.

Unlike the gravitational force, which is always attractive, the magnetic force can be either attractive or repulsive.

Unlike the gravitational case, single magnetic point sources (monopoles) can never be found alone in the magnetic case. Rather, monopoles always occur in pairs. A pair of magnetic monopoles, referred to as a dipole, always consists of one positive monopole and one negative monopole.

A properly reduced gravitational field is always generated by subsurface variations in rock density. A properly reduced magnetic field, however, can have as its origin at least two possible sources. It can be produced via an induced magnetization, or it can be produced via a remnant magnetization.

Unlike the gravitational field, which does not change significantly with time**, the magnetic field is highly time dependent.

gravity requires 0.1 ppm accuracy, magnetic > 10 ppm gravimeter is relative instrument; magnetometer is absolute

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densities vary from 1 to 4; susceptibility over several orders of magnitude

gravity anomalies smooth, regional; magnetic anomalies sharp, local

tides are only external gravity effect, can be corrected. Effect of magnetic storms cannot be removed.

gravity corrections: drift, latitude, free air, Bouguer, terrain, etc.; magnetic corrections: ± drift, IGRF

gravity surveys slow, expensive; magnetic costs about 1/10 of g

Applications of Rock magnetism in paleomagnetism :

a- Reversals of the earth’s field. (most recent reversal about 20.000

y. ago., 50/50 N/R. b- Sea floor spreading. c- Secular variation and paleo intensity of the earth field. d- Polar wander and continental drift. e- Paleo climatology. f- Magnetic dating of rocks by :

- secular variation 103 y. - polarity zones 104 – 106 y. - average paleomagnetic pole positions 107 – 109 y. - Q ratio.

g. Tectonic movements involving rotation. Ex. Japan. By NRM.

GENARAL APPLICATIONS

o Finding buried steel tanks and waste drums

o Detecting iron and steel obstructions

o Accurately mapping archaeological features

o Locating unmarked mineshafts

o Mapping basic igneous intrusives & faults

o Evaluating the size and shape of ore bodies

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Problem Sets

PROBLEM 1

IF THE MAGNETIC SUSCEPTIBILITY OF A SPHERICAL PLUTON IS 0.0003 AND THE EARTH’S MAGNETIC FIELD ( B ) IS 0.0006 TESLA. THE RADIUS OF THE PLUTON IS 1 KM AND THE MAGNETIC PERMEABILITY IS 4 π X 10 -7.

COMPUTE : 1. THE MAGNETIC FIELD STRENGTH ( H ) 2. THE INTENSITY OF MAGNETIZATION ( I ) 3. THE MAGNETIC MOMENT OF THE PLUTON ( M ).

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الإستكشاف السيزميمصطلحات

المصطلح الترجمة العربية المرونة

Elasticity

Stress System نظام الإجهاد Poisson’s ratio عامل بوايسونم

Tangential Stress الإجهاد المماسي Transverse Stress الإجهاد المستعرض

Transverse Strain التشوه )الانفعال( المستعرض Normal Stress الإجهاد العمودي Rigidity Modulus معامل الصلابة Shear Modulus معامل القص Hooke’s Law قانون هوك Elastic Limit حد المرونة Plastic Point نقطة اللدونة

Anelastic Materials المواد اللامرنة Shear resistance مقاومة القص Young’s modulus معامل يونج Compressibility الانضغاطية Dilatation تمدد حجمي

Wave Propagation الانتشار الموجي Body Waves الموجات الباطنية Surface Waves الموجات السطحية Longitudinal Waves الموجات الطولية Primary Waves الموجات الأولية

الموجات التضاغطيةCompressional Waves

Shear Waves موجات القص Transverse Waves موجات مستعرضة

Secondary Waves موجات ثانوية Birch’s Law قانون بيرش Seismic Velocities سرع سيزميه Rayleigh Waves (LR) موجات رايلي Love Waves (LQ) موجات لوف

Dispersion تشتت Amplitude سعة الموجة Wavelength طول الموجة

Frequency تردد

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Seismic Refraction الانكسار السيزمي Seismic Reflection الانعكاس السيزمي

Critical Distance ةالمسافة الحرج Thickness سماكة Depth عمق

Seismic Source مصدر سيزمي Transmitter مرسل Receiver مستقبل

Geophones سماعات أرضية مبدأ فيرمات

Fermat’s Principle

Huygen’s Principle مبدأ هايجن cReflection Coefficient (R( معامل الانعكاس

cTransmission Coefficient (T( مل الاختراقمعا Acoustic Impedance العائق الصوتي Wavefront مقدمة الموجة Raypath مسار الموجة Snell’s Law قانون سنيل

Critical Refraction الانكسار الحرج Low- Velocity – Layer طبقة منخفضة السرعة

Hidden Layer طبقة مختبئة Blind Layer ياءطبق عم

Thin Layer طبقة رقيقة Diffraction الحيود

Delay Time زمن التأخير Dipping Layers طبقات مائلة Green Equation معادلة جرين

Dynamic Correction التصحيح الديناميكي Multiple Reflection انعكاس متعدد

Time- Average Equation معادلة معدل الزمن معادلة فوست

Faust Equation

Apparent Velocity سرعة ظاهرية Average Velocity (VA) معدل سرعة Interval Velocity (VI) سرعة بينية

Root Mean Square Velocity سرعة تربيع متوسط الجذر Dix Equation معادلة ديكس

Data Processing معالجة المعلومات Cross Over Distance مسافة العبور Seismic Attenuation تعتيم سيزمي

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الإستكشاف مصطلحات الكهربائي

Self Potential جهد ذاتي

Galvanometer مقياس الجهد الكهربائي

Apparent Resistivity مقاومية ظاهرية

Equipotential line خط متساوي الجهد

Principle of Equivalence مبدأ التعادل

Principle of Suppression مبدأ الغطس

Conductivity التوصيلية

Vertical Electrical Sounding الجس الكهربائي العمودي

Horizontal Electrical Profiling المقطع الكهربائي الأفقي

Dipole ثنائي القطب

Schlumberger Arrangement ترتيب شلمبرجير

Induced Polarization الإستقطابية المستحثة

Passive Methods الطرق الخامدة

Electrical Conduction التوصيل الكهربائي

Archie's Law قانون أرشي

Electrical Reflection Coefficient معامل الإنعكاسية الكهربائية

Ground Penetrating Radar (GPR) رادار الإختراق الأرضي

Airborne Electromagnetic لجويالمسح الكهرومغناطيسي ا

Very Low Frequency (VLF) التردد المنخفض جدا

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الإستكشاف الجاذبي والمغناطيسيمصطلحات

Absolute gravity جاذبية مطلقة

Magnetic Field Strength قوة المجال المغناطيسي

Magnetic Induction الحث المغناطيسي

Centrifugal Force قوه طرد مركزية

Intensity of Magnetization شدة التمغنط

Magnetic Declination انحراف مغناطيسي

Diamagnetic ضعيف النفاذية المغناطيسية

Diurnal Correction تصحيح يومي

Elevation Correction تصحيح الارتفاع

Equator خط الاستواء

Magnetic Permeability النفاذية المغناطيسية

Ferro magnetic مغناطيس حديدي

Gravitational Acceleration التسارع الجاذبي

Gravity Anomaly شاذة الجاذبية

Magnetic Inclination الميل المغناطيسي

Isostatic Correction تصحيح ايزوستاتي

Lunar Variations تغيرات قمرية

Magnetic Moment العزم المغناطيسي

Magnetic Storms غناطيسيةعواصف م

Magnetometer جهاز قياس المغناطيسية

Magnetic Susceptibility قابلية مغناطيسية )التأثرية المغناطيسية(

Observed Gravity جاذبية مقاسة

Paleomagnetism مغناطيسية قديمة

Residual Magnetism مغناطيسية متخلفة

Remanent Magnetism مغناطيسية متبقية

Secular Variations تغيرات متناهية البطء

Geoid الجيوئد ) سطح متساوي الجهد (

Gravimeter جهاز قياس الجاذبية

Bouguer Anomaly شاذة بوجير

Latitude Correction تصحيح خط العرض